Question

Read and solve the problem below: <1, <2, and <3 form a straight line. If m<3 is six more than twice m<1 and m<2 is 27 less than m<3, find m<2

Answer 1

`m\angle 2=57^(\circ)`

Explanation:

Let x represent measure of angle 1.

We have been given that measure of angle 3 is six more than twice the measure of angle 1. So measure of angle 3 would be
`2x+6`.

We are also told that measure of angle 2 is 27 less than measure of angle 3, so measure of angle 2 would be
`2x+6-27\Rightarrow 2x-21`.

We have been given that angle 1, angle 2 and angle 3 form a straight line, so the sum of angles 1, 2 and 3 would be 180 degrees.

`m\angle 1+m\angle 2+m\angle 3=180^(\circ)`

Upon substituting the expressions for measure of angles, we will get:

`x+2x-21+2x+6=180`

Now, we will combine like terms.

`5x-15=180`

`5x-15+15=180+15`

`5x=195`

`(5x)/(5)=(195)/(5)`

`x=39`

The measure of angle 2 would be
`2x-21\Rightarrow 2(39)-21=78-21=57`.

Therefore, the measure of angle 2 is 57 degrees.