Question

what is the measure of angle b?

question 10 6.25 pts

set up an equation to find x.

Explanation:

Step1: Find the measure of angle \( a \)

Use the linear - pair property (sum of angles in a linear pair is \( 180^{\circ} \)).
\( a+117^{\circ}=180^{\circ}\)
\( a = 180^{\circ}-117^{\circ}=63^{\circ}\)

Step2: Find the measure of angle \( b \)

Use the triangle - angle sum property (sum of angles in a triangle is \( 180^{\circ} \)).
\( b + 81^{\circ}+a=180^{\circ}\)
Substitute \( a = 63^{\circ}\) into the equation:
\( b+81^{\circ}+63^{\circ}=180^{\circ}\)
\( b+144^{\circ}=180^{\circ}\)
\( b=180^{\circ}-144^{\circ}=36^{\circ}\)

Use the exterior - angle property of a triangle (an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles).
The exterior angle is \(2 + 12x\), and the two non - adjacent interior angles are \(42^{\circ}\) and \(8x\).
So, \(42+8x=2 + 12x\)

Answer:

\(36^{\circ}\)

For the second problem (setting up the equation for \(x\)):