Question

solve the following equations:

Explanation:

Step1: Recall angle - sum property

For the first figure with a right - angle and a 47° angle, since the sum of angles on a straight line is 180° and one angle is 90° and another is 47°, we have $b = 180-(90 + 47)$.
$b=180 - 137=43^{\circ}$

Step2: Use angle - bisector property

For the second figure with a 156° angle bisected into two equal parts, $b=\frac{156}{2}=78^{\circ}$

Step3: Use vertical - angle property

For the third figure, vertical angles are equal. If one angle is 50°, then $b = 50^{\circ}$

Step4: Use exterior - angle property

For the fourth figure, the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the exterior angle be 84°. Then $b = 84^{\circ}$

Answer:

First figure: $b = 43^{\circ}$
Second figure: $b = 78^{\circ}$
Third figure: $b = 50^{\circ}$
Fourth figure: $b = 84^{\circ}$