Question

1. In the figure, angle A is an exterior angle to triangle BCD.

(a) Explain why angle A is equal to the sum of the measures of the two nonadjacent interior angles. Show your work.
(b) What is the measure of angle A? Angle B? Show your work.

Answer 1

Comment
It has to do with supplementary angles.
Supplementary angles add up to 180o
A triangle has angles that always add up to 180o

Equations
First condition
<A + <CBD = 180o
<CBD + <C + <D = 180o

Since both left sides = 180o
The two left sides can be equated

<A + <CBD = <CBD + <C + <D Subtract <CBD from both sides.
<A = <C + <D which is what you needed to prove.

Angle sizes.
<A = <C + <D
<C = 65
<D = 55

<A = 65 + 55
<A = 120o <<<< 1st answer.
<B = 180 - 120
<B = 60o <<<<< 2nd answer.