Question

In the figure, x is an exterior angle to triangle ABC. (a) Explain why x is equal to the sum of the measures of the two nonadjacent interior angles. (b) What is m

Answer 1

Hello from MrBillDoesMath!

Answer:

a) See Discussion below

b) Don't know what "m" refers to

Discussion:

Part a)

A triangle contains 180 degrees.

A + B + C = 180   (*)

where A is the angle inside the triangle.

From the diagram

B +C =   62 + 78 = 140

Substituting this in (*) gives

A + (140) = 180      => subtract 140 from both sides

A = 180 - 140 = 40

Now a line has 180 degrees so x + A = 180. But A = 40 (shown above) so x+ 40 = 180, or x = 140. That is, x  = 140 - the sum of the measures of the two nonadjacent interior angles

Part b)

I can't answer this part is it is unclear what "m" refers to. Sorry.

Thank you,

MrB