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.