Question

PLS HELP ON MATH QUIZ PT.2

Answer 1

Given:

In the given figure, $m\angle 1=(3x+12)^\circ, m\angle 2=(3x+18)^\circ, m\angle 3=(7x+10)^\circ$.

To find:

The measure of angle 3.

Solution:

According to the exterior angle theorem of a triangle, the measure of exterior angle is equal to the sum of two opposite interior angles of a triangle.

Using exterior angle theorem of a triangle, we get

$m\angle 3=m\angle 1+m\angle 2$

$7x+10=(3x+12)+(3x+18)$

$7x+10=6x+30$

$7x-6x=30-10$

$x=20$

The value of x is 20. So, the measure of angle 3 is:

$m\angle 3=(7x+10)^\circ$

$m\angle 3=(7(20)+10)^\circ$

$m\angle 3=(140+10)^\circ$

$m\angle 3=150^\circ$

Therefore, the measure of angle 3 is 150 degrees.