KETHLEDGE, Circuit Judge.
Del Tonguette died during a 91-day period in which, under the terms of an ERISA plan, he was entitled to convert his group life-insurance policy to an individual one. His widow, Diane Tonguette, thereafter requested payment of Del’s life-insurance benefit. The plan’s administrator, Sun Life — which is also the insurer that would pay the benefit — denied payment under its reading of the plan’s terms. Di[546]*546ane later brought this lawsuit under ERISA, 29 U.S.C. § 1132(a), claiming that Sun Life’s denial was contrary to the plan’s terms. The district court granted summary judgment to Sun Life. We reverse.
Del Tonguette began work at LoBue Associates in August 2009. LoBue maintains an ERISA benefits plan administered by Sun Life. Under that plan, Del’s benefits package included group life-insurance coverage in the amount of $95,000. Del left LoBue’s employ on October 16, 2009, at which time, per the terms of the group policy, his coverage ended. But the plan gave Del the option to convert his group life-insurance policy to an individual one. As a general matter, under the plan, that option remains available only for 81 days. That period is extended to 91 days, however, if neither LoBue nor Sun Life provides a departing employee with notice of the option.
Del Tonguette neither received notice of his conversion option nor exercised it before he died. That Del did not receive notice of his conversion option means that his conversion period ran for the full 91 days, until January 15, 2010. But Del died six days before then, on January 9, 2010. His widow, Diane Tonguette (whom we refer to as “Tonguette”), thereafter requested payment of his death benefit under the group policy, citing a plan provision entitled “Death within the Conversion Period.” The plan’s administrator, Sun Life, read that provision differently and denied payment. The district court agreed with Sun Life’s reading. Ton-guette appealed.
LoBue’s plan gives Sun Life discretion with respect to its determinations whether a plan participant is eligible for benefits. To the extent a plan administrator exercises such discretion in denying a claim for benefits, we uphold its decision so long as the decision is not arbitrary or capricious. Kovach v. Zurich Am. Ins. Co., 587 F.3d 323, 328 (6th Cir.2009). But a plan administrator does not have discretion to adopt an interpretation of the plan contrary to its unambiguous terms. Adams v. Anheuser-Busch Companies, Inc., 758 F.3d 743, 747-48 (6th Cir.2014). And “[w]hether plan language is ambiguous is a legal question that we review de novo.” Id. at 747. Finally, in determining whether plan language is ambiguous, “we apply federal common law rules of contractual interpretation[.]” Perez v. Aetna Life Ins. Co., 150 F.3d 550, 556 (6th Cir.1998) (en banc).
The provision at the heart of the dispute here provides in full:
Death within the Conversion Period
Claim may be made for a death benefit if you die during the SI day period during which your insurance may be converted to an individual policy. (See section “Conversion Privilege”.)
The terms of this benefit are as follows:
1. The amount of your Life Insurance that may be converted will be payable as a claim under the group policy. No Accidental Death and Dismemberment benefit, if any, will be paid under the terms of this section.
2. This benefit will apply whether or not you have:
a) applied for a conversion policy; or
b) paid the first premium.
3. If a conversion policy has been issued:
a) it must be given back to the insurer; and
b) no claim can be made under it other than for the return of premiums paid.
(Italicization added.)
Under this provision, if a plan participant dies within the period described by [547]*547the italicized language, Sun Life will pay the participant’s death benefit (in Del’s case $95,000) under the group insurance policy. The dispute here concerns the length of the period described by the italicized language. Specifically, as the parties acknowledged at oral argument, the question presented is whether the italicized language refers to the length of the applicable conversion period under the plan (Tonguette’s view), or instead refers only to the first 31 days following the termination of group coverage, even if the conversion period runs longer than 31 days (Sun Life’s view).
The meaning of this language is . straightforward in cases where the plan participant is given notice of the conversion option: under either Tonguette’s view or Sun Life’s, the italicized language refers to a single 31-day period that begins on the date the participant leaves the company. But — at least when considered in isolation — the italicized language becomes grammatically incoherent in cases where, as here, the conversion period extends beyond 31 days. The language refers to “the 31 day period during which your insurance may be converted to an individual policy.” As used in this clause, “the” is a definite article, meaning there is only one 31-day period in which the participant can convert. In cases where the conversion period is more than 31 days, however, there is more than one 31-day period in which the participant can convert. For example, in a case where the period runs for 33 days, there are three such 31-day periods: one from days 1-31, a second from days 2-32, and a third from days 3-33. In Del’s case, where the conversion period ran for 91 days, there were 61 different 31-day periods — starting as early as day 1 and as late as day 61 — in which he could have converted. Thus, in these cases, the grammatical premise of the italicized language — that there is only one 31-day period in which the participant can convert — is absent.
The parties try to resolve this incoherency by, in effect, adding one word or subtracting two, respectively, from the italicized language. Sun Life would add a word, reading this language to mean “the initial 31 day period during which your insurance may be converted to an individual policy.” Tonguette would subtract the words “31 day”, reading the language to mean “the [] period during which your insurance may be converted to an individual policy.”
Read in isolation, then, the italicized language appears ambiguous. This ambiguity recedes, however, when one looks at the language of the relevant “Part” of the plan as a whole. That language includes two indications as to how to resolve the incoherency here — and both of them favor Tonguette’s interpretation. The first is the provision’s heading, which cannot be used to create ambiguity, but can be used to resolve it. See, e.g., Int’l Multifoods Corp. v. Comm’l Union Ins. Co., 309 F.3d 76, 85 (2d Cir.2002).
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KETHLEDGE, Circuit Judge.
Del Tonguette died during a 91-day period in which, under the terms of an ERISA plan, he was entitled to convert his group life-insurance policy to an individual one. His widow, Diane Tonguette, thereafter requested payment of Del’s life-insurance benefit. The plan’s administrator, Sun Life — which is also the insurer that would pay the benefit — denied payment under its reading of the plan’s terms. Di[546]*546ane later brought this lawsuit under ERISA, 29 U.S.C. § 1132(a), claiming that Sun Life’s denial was contrary to the plan’s terms. The district court granted summary judgment to Sun Life. We reverse.
Del Tonguette began work at LoBue Associates in August 2009. LoBue maintains an ERISA benefits plan administered by Sun Life. Under that plan, Del’s benefits package included group life-insurance coverage in the amount of $95,000. Del left LoBue’s employ on October 16, 2009, at which time, per the terms of the group policy, his coverage ended. But the plan gave Del the option to convert his group life-insurance policy to an individual one. As a general matter, under the plan, that option remains available only for 81 days. That period is extended to 91 days, however, if neither LoBue nor Sun Life provides a departing employee with notice of the option.
Del Tonguette neither received notice of his conversion option nor exercised it before he died. That Del did not receive notice of his conversion option means that his conversion period ran for the full 91 days, until January 15, 2010. But Del died six days before then, on January 9, 2010. His widow, Diane Tonguette (whom we refer to as “Tonguette”), thereafter requested payment of his death benefit under the group policy, citing a plan provision entitled “Death within the Conversion Period.” The plan’s administrator, Sun Life, read that provision differently and denied payment. The district court agreed with Sun Life’s reading. Ton-guette appealed.
LoBue’s plan gives Sun Life discretion with respect to its determinations whether a plan participant is eligible for benefits. To the extent a plan administrator exercises such discretion in denying a claim for benefits, we uphold its decision so long as the decision is not arbitrary or capricious. Kovach v. Zurich Am. Ins. Co., 587 F.3d 323, 328 (6th Cir.2009). But a plan administrator does not have discretion to adopt an interpretation of the plan contrary to its unambiguous terms. Adams v. Anheuser-Busch Companies, Inc., 758 F.3d 743, 747-48 (6th Cir.2014). And “[w]hether plan language is ambiguous is a legal question that we review de novo.” Id. at 747. Finally, in determining whether plan language is ambiguous, “we apply federal common law rules of contractual interpretation[.]” Perez v. Aetna Life Ins. Co., 150 F.3d 550, 556 (6th Cir.1998) (en banc).
The provision at the heart of the dispute here provides in full:
Death within the Conversion Period
Claim may be made for a death benefit if you die during the SI day period during which your insurance may be converted to an individual policy. (See section “Conversion Privilege”.)
The terms of this benefit are as follows:
1. The amount of your Life Insurance that may be converted will be payable as a claim under the group policy. No Accidental Death and Dismemberment benefit, if any, will be paid under the terms of this section.
2. This benefit will apply whether or not you have:
a) applied for a conversion policy; or
b) paid the first premium.
3. If a conversion policy has been issued:
a) it must be given back to the insurer; and
b) no claim can be made under it other than for the return of premiums paid.
(Italicization added.)
Under this provision, if a plan participant dies within the period described by [547]*547the italicized language, Sun Life will pay the participant’s death benefit (in Del’s case $95,000) under the group insurance policy. The dispute here concerns the length of the period described by the italicized language. Specifically, as the parties acknowledged at oral argument, the question presented is whether the italicized language refers to the length of the applicable conversion period under the plan (Tonguette’s view), or instead refers only to the first 31 days following the termination of group coverage, even if the conversion period runs longer than 31 days (Sun Life’s view).
The meaning of this language is . straightforward in cases where the plan participant is given notice of the conversion option: under either Tonguette’s view or Sun Life’s, the italicized language refers to a single 31-day period that begins on the date the participant leaves the company. But — at least when considered in isolation — the italicized language becomes grammatically incoherent in cases where, as here, the conversion period extends beyond 31 days. The language refers to “the 31 day period during which your insurance may be converted to an individual policy.” As used in this clause, “the” is a definite article, meaning there is only one 31-day period in which the participant can convert. In cases where the conversion period is more than 31 days, however, there is more than one 31-day period in which the participant can convert. For example, in a case where the period runs for 33 days, there are three such 31-day periods: one from days 1-31, a second from days 2-32, and a third from days 3-33. In Del’s case, where the conversion period ran for 91 days, there were 61 different 31-day periods — starting as early as day 1 and as late as day 61 — in which he could have converted. Thus, in these cases, the grammatical premise of the italicized language — that there is only one 31-day period in which the participant can convert — is absent.
The parties try to resolve this incoherency by, in effect, adding one word or subtracting two, respectively, from the italicized language. Sun Life would add a word, reading this language to mean “the initial 31 day period during which your insurance may be converted to an individual policy.” Tonguette would subtract the words “31 day”, reading the language to mean “the [] period during which your insurance may be converted to an individual policy.”
Read in isolation, then, the italicized language appears ambiguous. This ambiguity recedes, however, when one looks at the language of the relevant “Part” of the plan as a whole. That language includes two indications as to how to resolve the incoherency here — and both of them favor Tonguette’s interpretation. The first is the provision’s heading, which cannot be used to create ambiguity, but can be used to resolve it. See, e.g., Int’l Multifoods Corp. v. Comm’l Union Ins. Co., 309 F.3d 76, 85 (2d Cir.2002). And here the provision’s heading resolves the ambiguity cleanly, by making clear that the italicized language refers to, as the heading says, “death within the conversion period.”
The second indication comes in a provision entitled “Notice of Conversion Period[,]” which provides in relevant part: “Written notice of the Conversion Privilege and its duration will be given to you at least 15 days before the end of the 31 day period following termination of coverage under the Group Policy.” (Emphasis added). This italicized language — which comes in the very next provision after the one at issue here — conveys exactly the same meaning that Sun Life tries to give to “the 31 day period during which your insurance may be converted to an individual policy” in the preceding provision. And [548]*548that the two provisions use markedly different language, in such close proximity, is reason to read them differently. See, e.g., Smith v. ABS Industries, Inc., 890 F.2d 841, 846 (6th Cir.1989).
One might respond that Tonguette’s reading of the plan allows her to obtain a death benefit even though Del paid no premiums for almost three months after his group coverage terminated, rather than just one month. But that is an equitable point, not a textual one; and even taken on its own terms, the equities of that point are offset by the greater dereliction of failing to provide notice of the conversion option for three months, rather than just one. That dereliction is significant in part because a person losing his insurance could easily overlook that his policy— which he might have bought years earlier — even includes a conversion option.
In summary, when read in the broader context of the plan, there are two significant reasons to favor Tonguette’s reading of the disputed language, and none to favor Sun Life’s. Moreover, there is a difference between vague terms — whose vagueness might give rise to discretion— and poorly drafted terms that, after a careful reading, demonstrably favor one interpretation over another. Here, a careful reading of the plan’s terms reveals that Tonguette’s interpretation is demonstrably better than Sun Life’s. As a plan fiduciary, Sun Life was obligated to read the plan carefully; and it lacked discretion to reject Tonguette’s interpretation of the disputed language here. Its interpretation therefore was arbitrary and capricious.
The district court’s judgment is reversed, and the case remanded for proceedings consistent with this opinion.