Question

The angle measurements in the diagram are represented by the following expressions.

ZA = 10x + 24°
B = 6x + 72
Solve for 3 and then find the measure of ZA:

Answer 1

Given:

`\angle A=10 x+24^(\circ)`

`\angle B=6 x+72^(\circ)`

To find:

The value of x and measure of ∠A.

Solution:

Let C be angle the vertically opposite to ∠A.

The reference image for answer is attached below.

By vertical angle theorem:

m∠A = m∠C

m∠C = 10x + 24°

By the corresponding angle theorem:

m∠C = m∠B

`10x + 24^\circ = 6x+72^\circ`

Subtract 24° on both sides.

`10x = 6x+48^\circ`

Subtract 6x from both sides.

`4x=48^\circ`

Divide by 4 on both sides.

`x = 12^\circ`

The value of x is 12°.

`\angle A=10 x+24^(\circ)`

`=10 (12^(\circ))+24^(\circ)`

`=144^\circ`

The measure of ∠A is 144°.