Question

!!!!! Please help !!!!!!
Explain work too please so I can understand better

Answer 1

m∠P = 116°

m∠Q = 21°

m∠R = 43°

Explanation:

To solve, remember that the sum of all angles in any triangle is 180°. So, m∠P+m∠Q+m∠R=180°.

The problem states:

m∠P = (5x-14)°

m∠Q = (x-5)°

m∠R = (2x-9)°

So, for this problem,

`(5x-14)+(x-5)+(2x-9)=180\\5x+x+2x-14-5-9=180\\8x-28=180\\8x-28+28=180+28\\8x=208\\((1)/(8))8x=208((1)/(8))\\x=26`

Use this value of x and the given conditions to find each angle measure:

m∠P = [5(26)-14]° = 116°

m∠Q = [(26)-5]° = 21°

m∠R = [2(26)-9]° = 43°

To check:

116°+21°+43°=180°

180°=180°