Question

The measure of ∠2 is twelve less than five times the measure of ∠1. If ∠1 and ∠2 form a linear pair, find m∠2.

Answer 1

Given:

The measure of ∠2 is twelve less than five times the measure of ∠1.

∠1 and ∠2 form a linear pair.

To find:

The measure of ∠2.

Solution:

Let measure of ∠1 be x.

The measure of ∠2 is twelve less than five times the measure of ∠1.

$m\angle 2=(5(m\angle 1)-12)^\circ$

$m\angle 2=(5x-12)^\circ$

∠1 and ∠2 form a linear pair. So,

$m\angle 1+m\angle 2=180^\circ$

$x^\circ+(5x-12)^\circ=180^\circ$

$6x-12=180$

$6x=180+12$

$6x=192$

Divide both sides by 6.

$x=32$

Now,

$m\angle 2=(5(32)-12)^\circ$

$m\angle 2=(160-12)^\circ$

$m\angle 2=148^\circ$

Therefore, the measure of angle 2 is 148 degrees.