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.

Accepted Solution

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

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.