Question

Find the measure of the missing angles. 83°C b

Answer 1

Answer:

$m\angle b=97^{\circ},\\m\angle c= 97^{\circ}$

Step-by-step explanation:

Vertical angles are angles on opposites sides of an intersection of two lines. Therefore, $\angle c$ and $\angle b$ are vertical angles. Similarly, the angle opposite to the angle marked 83 degrees is also equal to 83 degrees. Vertical angles are always equal.

Since there are 360 degrees in a circle, we have the following equation:

$\angle c+\angle b+83+83=360,\\2\angle c+166=360,\\2\angle c=194,\\\angle c=\frac{194}{2}=\boxed{97^{\circ}}$

Since $\angle c$ and $\angle b$ are vertical angles and vertical angles are also equal, the measure of angle $b$ is also $\boxed{97^{\circ}}$