Question

current skill $ find the measure of angle 8. 1 2 4 5x + 17 5 6 8 -8x + 134

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Angle 1 and the angle with measure $5x + 17$ are vertical angles, and angle 5 and the angle with measure $-8x + 134$ are vertical angles. Also, angle 1 and angle 5 are corresponding angles (assuming the lines are parallel, which is a common context for such angle - finding problems), so $5x+17=-8x + 134$.

Step2: Solve the equation for x

Add $8x$ to both sides of the equation $5x+17=-8x + 134$:
$5x+8x+17=-8x+8x + 134$
$13x+17 = 134$
Subtract 17 from both sides:
$13x+17-17=134 - 17$
$13x=117$
Divide both sides by 13:
$x=\frac{117}{13}=9$

Step3: Find the measure of angle 5

Substitute $x = 9$ into the expression for the measure of angle 5 (which is equal to $-8x + 134$).
$-8\times9+134=-72 + 134 = 62$

Step4: Find the measure of angle 8

Angle 5 and angle 8 are vertical angles. Since vertical angles are equal, the measure of angle 8 is also 62.

Answer:

62