How big was the third angle?

Question

Mr.Riggle drew a triangle such that the first angle was three times as much as the second angle, and the third angle 40° more than the first. How big was the third angle

Answer 1

This problem is going to given you a system of 3 linear equations in 3 unknowns.

 

Let A = ∠!, B = ∠2 and C = ∠3

 

A = 3B, C = A + 40, A + B + C = 180

Write this is the usual form

 

A + B + C =180

A - 3B = 0

-A + C = 40

 

Add the last equation to each of the other 2

B + 2C = 220

-3B + C = 40

 

B + 2C = 220

-6B + 2C = 80

 

Subtract the bottom equation from the top

7B = 140

B = 20

A = 60

C = 100