Discussion
The difference of two complementary angles is 40°. If smaller of these angles is y, then the value of \((2y + 15^{\circ})\) is
Answer: D
The value of (2y + 15°) is 65°.
Complementary angles add up to 90°. Let the larger be a and the smaller y:
\[ \begin{aligned} a + y &= 90^{\circ},\ a - y = 40^{\circ} \\ y &= 25^{\circ} \\ 2y + 15^{\circ} &= 65^{\circ} \end{aligned} \]
The angles are 65° and 25°, and they do add to 90° and differ by 40°. Note that 2y + 15° happens to equal the larger angle, a useful check. Any other value of y breaks one of the two conditions, so 45°, 50° and 55° are wrong.
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