two parallel lines are crossed by a transversal. what is the value of b? o b = 32 o b = 52 o b = 118 o b = 128
two parallel lines are crossed by a transversal. what is the value of b? o b = 32 o b = 52 o b = 118 o b = 128
Answer
Explanation:
Step1: Identify angle - relationship
When two parallel lines are crossed by a transversal, corresponding angles are equal. The angle adjacent to the (128^{\circ}) angle and angle (b) are corresponding angles. First, find the adjacent - angle to (128^{\circ}). The adjacent - angle to (128^{\circ}) and (128^{\circ}) form a linear pair. A linear pair of angles sum to (180^{\circ}). Let the adjacent - angle to (128^{\circ}) be (x). Then (x + 128^{\circ}=180^{\circ}). So, (x=180^{\circ}-128^{\circ}=52^{\circ}).
Step2: Determine the value of (b)
Since (b) and (x) are corresponding angles (because (p\parallel q) and (m) is the transversal), (b = x). So, (b = 52^{\circ}).
Answer:
(b = 52)