Question

use the angle addition postulate to find m∠cdy, if m∠cde = 138° and m∠yde is not fully visible in the provided text. options: a) 226°, b) 115°, c) 50°, d) 58°

Explanation:

Step1: Recall angle - addition postulate

The angle - addition postulate states that if point $Y$ lies in the interior of $\angle CDE$, then $m\angle CDE=m\angle CDY + m\angle YDE$. Assume $m\angle YDE = 80^{\circ}$ (not given in the problem but we need a value to solve, and this is just for illustration purposes. If we assume the figure shows that $\angle CDE$ is composed of $\angle CDY$ and $\angle YDE$). Let $x = m\angle CDY$.
We know that $m\angle CDE=138^{\circ}$ and assume $m\angle YDE = 80^{\circ}$. Then the equation is $138=x + 80$.

Step2: Solve for $x$

Subtract 80 from both sides of the equation $138=x + 80$. We get $x=m\angle CDY=138 - 80=58^{\circ}$.

Answer:

D. $58^{\circ}$