Answer:
[tex]x = 20^{\circ}[/tex]
[tex]\angle A = 150^{\circ}[/tex]
Step-by-step explanation:
Given
[tex]\angle A = 8x - 10[/tex]
[tex]\angle B = 3x + 90[/tex]
See attachment
From the attachment A and B are vertically opposite.
This implies that:
[tex]\angle A = \angle B[/tex]
Substitute values for A and B
[tex]8x - 10 = 3x + 90[/tex]
Collect Like Terms
[tex]8x - 3x = 10 + 90[/tex]
[tex]5x = 100[/tex]
Solve for x
[tex]x = \frac{100}{5}[/tex]
[tex]x = 20^{\circ}[/tex]
Substitute 20 for x in [tex]\angle A = 8x - 10[/tex]
[tex]\angle A = 8 * 20 - 10[/tex]
[tex]\angle A = 150^{\circ}[/tex]
