At Bishan Park, two straight flagpole wires cross at point P, forming two pairs of vertically opposite angles. Two of the angles at P are (3a + 7)° and (a + 33)°. A ray PQ is drawn from P, and triangle PQR is formed. The angle PQR = 73° and angle QPR equals the smaller of the two vertically opposite angles formed by the crossing wires. Find angle PRQ.
Show Worked Solution
Worked Solution
Step 1: Since the two angles are vertically opposite, they are equal:
3a + 7 = a + 33
2a = 26
a = 13
Step 2: Find angle QPR (the smaller vertically opposite angle):
angle QPR = 3(13) + 7 = 39 + 7 = 46°
Step 3: Apply angle sum of triangle PQR:
angle PRQ = 180° − angle PQR − angle QPR
angle PRQ = 180° − 73° − 46° = 61°
Correct answer: 61°
Want more questions like this? Superholic Lab has 10,000+ MOE-aligned questions with full worked solutions.
Start Free Trial — 7 Days Free