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Question

# Determine the measure of each angle. Show your work and explain your reasoning. a. Two angles are congruent and supplementary. b. Two angles are congruent and complementary. c. The complement of an angle is twice the measure of the angle. d. The supplement of an angle is half the measure of the angle.

Solution

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### Part (a)

If two angles are congruent then they have equal measure. Moreover, if they are supplementary, sum of their measures is $180^\circ$.

$\begin{array}{l} x + x = 180^\circ \\ \\ 2x = 180^\circ \\ \\ x = \dfrac{{180^\circ }}{2}\\ \\ {\color{#001227}\boxed{\boxed{x = 90^\circ }}} \end{array}$

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