Question

In the diagram mz3= x+ 30 and mz4 =2x-80. What is the measure of angle 3?

Answer 1

Given:

Consider the below figure attached with this question.

$m\angle 3=(x+30)^\circ$ and $m\angle 4=(2x-80)^\circ$.

To find:

The measure of angle 3.

Solution:

From the below figure it is clear that, angle 3 and angle 4 are vertically opposite angles.

We know that, vertically opposite angles are always equal. So,

$m\angle 3=m\angle 4$

$(x+30)^\circ=(2x-80)^\circ$

$x+30=2x-80$

$x-2x=-30-80$

$-x=-110$

$x=110$

Now,

$m\angle 3=(110+30)^\circ$

$m\angle 3=140^\circ$

Therefore, the measure of angle 3 is 140 degrees.