Question

a carpenter is building a frame. which values of a and b will ensure that the sides of the finished frame are parallel?
○ a = 40 and b = 60
○ a = 45 and b = 50
○ a = 30 and b = 60
○ a = 40 and b = 40

Explanation:

Step1: Recall parallel - line property

For the sides of the frame to be parallel, the adjacent angles must be supplementary, i.e., \(a + b=90^{\circ}\).

Step2: Check each option

• Option 1: If \(a = 40\) and \(b = 60\), then \(a + b=40 + 60=100

eq90\).

• Option 2: If \(a = 45\) and \(b = 50\), then \(a + b=45+50 = 95

eq90\).

• Option 3: If \(a = 30\) and \(b = 60\), then \(a + b=30 + 60=90\).
• Option 4: If \(a = 40\) and \(b = 40\), then \(a + b=40+40 = 80

eq90\).

Answer:

\(a = 30\) and \(b = 60\)