In the diagram above, |PQ| = |PR| = |RS| and ∠RPS = 32^\circ. Find the value of ∠QPR
Attached Figure / Diagram
A
72o
B
64o
C
52o
D
32o
E
26o
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
From the figure, < PSR = 32^\circ (base angles of an isos. triangle)
\(\therefore\) < PRS = 180^\circ - (32^\circ + 32^\circ) = 116^\circ (sum of angles in a triangle)
< QRP = 180^\circ - 116^\circ = 64^\circ (angle on a straight line)
< PQR = 64^\circ (base angles of an isos. triangle)
< QPR = 180^\circ - (64^\circ + 64^\circ) = 52^\circ
Source: Myschool Past Questions Archive (Record #22672)