Library / UKMT Grey Kangaroo /225 of 242

UKMT Grey Kangaroo, 2023

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

In the diagram shown, sides $PQ$ and $PR$ are equal. Also $\angle QPR = 40^\circ$ and $\angle TQP = \angle SRQ$ . What is the size of $\angle TUR$ ?

(A) $55^\circ$ (B) $60^\circ$ (C) $65^\circ$ (D) $70^\circ$ (E) $75^\circ$

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.