In the diagram above, ∠PTQ = ∠URP = 25^\circ and XPU = 4URP. Calculate ∠USQ.
Attached Figure / Diagram
A
100o
B
120o
C
125o
D
130o
E
150o
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Since < URP = 25^\circ, then < XPU = 4 x 25^\circ = 100^\circ
\(\therefore\) < TPQ = 180^\circ - 100^\circ = 80^\circ
\(\therefore\) < PQT = 180^\circ - (80^\circ + 25^\circ) = 75^\circ
< SQR = 75^\circ - 25^\circ = 50^\circ (exterior angle = 2 opp interior angles)
\(\therefore\) < USQ = 180^\circ - 50^\circ = 130^\circ
Source: Myschool Past Questions Archive (Record #23110)