Question

In the diagram, the measure of angle 1 is (3x)°, and the measure of angle 2 is (12x)°.

What is the measure of angle 4?
36°
45°
135°
144°

Answer 1

3x+12x=180
15x=180
x=12
angle 2 = angle 4
angle 4= 12x =12*(12)=144

Answer 2

`m<4=144\°`

Explanation:

Step 1

Find the value of x

we know that

`m<1+m<2=180\°` -----> by supplementary angles

we have

`m<1=3x\°`

`m<2=12x\°`

substitute and solve for x

`3x+12x=180\°`

`15x=180\°`

`x=12\°`

Step 2

Find the measure of angle 4

we know that

`m<4=m<2` -----> by vertical angles

we have

`m<2=12x\°` ----->
`m<2=12(12)=144\°`

therefore

`m<4=144\°`