Question

The measure of ∠2=8x+10 and the measure of ∠4=42+6x. Find the measure of ∠4. Show your work and label your answer

Answer 1

Find out the measure of ∠4.

To prove

As given

The measure of ∠2=8x+10 and the measure of ∠4=42+6x .

Now as shown in the diagram

∠ 2 = ∠ 4

( By using the property of vertically opposite angle)

Thus

8x + 10 = 42 + 6x

2x = 32

`x = (32)/(2)`

x = 16

Put value of x in

∠4 = 42+6x.

∠4 = 42 + 6 × 16

∠4 = 42 + 96

∠4 = 138°

Therefore ∠4 =∠2= 138°

Hence proved