Question

1. in the figure below, lines p and q are parallel. the measure of ∠3 = 126°. what is the measure of all of the angles shown?

Explanation:

Step1: Find ∠1 and ∠2

• ∠1 and ∠3 are supplementary (linear - pair).

$$\angle1 = 180^{\circ}-\angle3=180^{\circ}- 126^{\circ}=54^{\circ}$$

• ∠2 and ∠3 are vertical angles.

$$\angle2=\angle4 = 54^{\circ}$$

Step2: Use parallel - line properties

• Since \(p\parallel q\), ∠2 and ∠6 are corresponding angles. So \(\angle6=\angle2 = 54^{\circ}\).
• ∠5 and ∠2 are alternate - interior angles. So \(\angle5=\angle2 = 54^{\circ}\).
• ∠7 and ∠3 are corresponding angles. So \(\angle7=\angle3 = 126^{\circ}\).
• ∠8 and ∠3 are alternate - interior angles. So \(\angle8=\angle3 = 126^{\circ}\).

Answer:

\(\angle1 = 54^{\circ},\angle2 = 54^{\circ},\angle4 = 54^{\circ},\angle5 = 54^{\circ},\angle6 = 54^{\circ},\angle3 = 126^{\circ},\angle7 = 126^{\circ},\angle8 = 126^{\circ}\)