Answer:
101.8°, 78.2°
Step-by-step explanation:
You want the measures of the two angles such that the larger is 23.6° more than its supplement.
Angle
Let x represent the larger angle. The given relation is ...
x = 23.6° +(180° -x)
2x = 180° +23.6°
x = (180° +23.6°)/2 = 101.8°
101.8° -23.6° = 78.2°
The two angles are 101.8° and 78.2°.
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Additional comment
This is a "sum and difference" problem, where the sum of the angles is 180°, and their difference is given as 23.6°. The solutions to such a problem are half the sum and difference of the sum and difference:
a + b = s . . . . sum
a - b = d . . . . difference
Adding: 2a = (s +d) ⇒ a = (s +d)/2
Subtracting: 2b = (s -d) ⇒ b = (s -d)/2
