Question

Find the measure of each angle


m
m

Answer 1

Answer:

47º

133º

Step-by-step explanation:

The sum of the angles is 180º

(3x + 5) + (10x - 7) = 180

Combine like terms

13x - 2= 180

Add 2 to both sides

13x = 182

Divide both sides by 13

x = 14

3(14) + 5 = 47º

10(14) - 7= 133º

Answer 2

 

TRQ and TRS angles are additional angles.

$\displaystyle\bf\\(3x+5)^o + (10x-7)^o=180^o\\\\3x+10x+5-7=180\\\\13x-2=180\\\\13x=180+2\\\\13x=182\\\\x=\frac{182}{13}\\\\\boxed{\bf x=14^o}\\\\m(\angle TRQ)=(3x+5)=3\cdot14+5=42+5\\\\\boxed{\bf m(\angle TRQ)=47^o}\\\\m(\angle TRS)=(10x-7)=10\cdot14-7=140-7\\\\\boxed{\bf m(\angle TRS)=133^o}$