The sum of the measures of two complementary angles exceeds the difference of their measures by 86°. Find the measure of the larger angle.

Complementary angles add to 90°. Since their sum exceeds their difference by 86°, the difference is 90° − 86° = 4°. The larger angle is half the sum plus half the difference: (90° + 4°) ÷ 2 = 47°, so the larger angle is 47°.

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