Question

what is the measure of angle b? 51° 117° 55° 63° 36° 117°

Explanation:

Step1: Find angle a

Since a straight - line angle is 180°, and one part of the straight - line is 117°, then $a = 180^{\circ}-117^{\circ}=63^{\circ}$.

Step2: Use triangle angle - sum property

The sum of angles in a triangle is 180°. In the triangle with angles 81°, a, and b, we know $81^{\circ}+a + b=180^{\circ}$. Substitute $a = 63^{\circ}$ into the equation: $81^{\circ}+63^{\circ}+b = 180^{\circ}$. Then $b=180^{\circ}-(81^{\circ}+63^{\circ})=180^{\circ}-144^{\circ}=36^{\circ}$.

Answer:

$36^{\circ}$