Question

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

Answer 1

`m\angle b=97^(\circ),\\m\angle c= 97^(\circ)`

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=(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)}`