Given:
[tex]\angle A=10 x+24^{\circ}[/tex]
[tex]\angle B=6 x+72^{\circ}[/tex]
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
[tex]10x + 24^\circ = 6x+72^\circ[/tex]
Subtract 24° on both sides.
[tex]10x = 6x+48^\circ[/tex]
Subtract 6x from both sides.
[tex]4x=48^\circ[/tex]
Divide by 4 on both sides.
[tex]x = 12^\circ[/tex]
The value of x is 12°.
[tex]\angle A=10 x+24^{\circ}[/tex]
[tex]=10 (12^{\circ})+24^{\circ}[/tex]
[tex]=144^\circ[/tex]
The measure of ∠A is 144°.
