Question

Find a,b, c, and d.

Answer 1

According to the given diagram, d and 46° are vertical angles, which means d = 46°.

Then, using the supplementary angles theorem, we have

$\begin{gathered} d+82+b=180 \\ 46+b+82=180 \\ b=180-46-82 \\ b=52 \end{gathered}$

On the other hand, a and 134 are vertical angles, so a = 134°.

Then, using the exterior angle theorem, we have

$\begin{gathered} a=b+c \\ 134=52+c \\ c=134-52 \\ c=82 \end{gathered}$

Hence, a = 134°, b = 52°, c = 82°, and d = 46°.