Question

11 mark for review
note: figure not drawn to scale.
in the figure above, lines m and n are parallel. what is the value of b?
40
50
65

Explanation:

Step1: Find the value of \(a\)

Since the angle of \(130^{\circ}\) and \(2a\) are supplementary (linear pair), \(2a + 130^{\circ}=180^{\circ}\).
So, \(2a=180^{\circ}- 130^{\circ}=50^{\circ}\), then \(a = 25^{\circ}\).

Step2: Use the property of parallel lines

Because lines \(m\) and \(n\) are parallel, and \(l\) is a transversal.
We know that \(90^{\circ}+a + b=180^{\circ}\) (sum of angles on a straight - line formed by the transversal with respect to the parallel lines).
Substitute \(a = 25^{\circ}\) into the equation: \(90^{\circ}+25^{\circ}+b=180^{\circ}\).
Then \(b=180^{\circ}-(90^{\circ}+25^{\circ})=65^{\circ}\).

Answer:

C. \(65\)