Question

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

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°.