Wei Lin draws two parallel lines l1 and l2. A transversal crosses l1 at point P and l2 at point Q. She labels angle BPQ = (3y − 5)°, where B is on l1 to the right of P, and angle PQC = (2y + 15)°, where C is on l2 to the right of Q. She then draws segment PR to a point R on l2 such that R is to the right of Q and angle QPR = 28°. What is angle PRQ?
Show Worked Solution
Worked Solution
Step 1: Co-interior angles (same side of transversal PQ, between parallel lines).
(3y − 5) + (2y + 15) = 180
5y + 10 = 180
y = 34
Step 2: angle PQC = 2(34) + 15 = 83°
Step 3: R is on l2 to the right of Q, so angle PQR = angle PQC = 83°.
Step 4: Triangle PQR angle sum.
28° + 83° + angle PRQ = 180°
angle PRQ = 69°
Correct answer: 69°
Want more questions like this? Superholic Lab has 10,000+ MOE-aligned questions with full worked solutions.
Start Free Trial — 7 Days Free