Library / UKMT Junior Kangaroo /119 of 243

UKMT Junior Kangaroo, 2017

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

In trapezium $PQRS$ , $\angle RSP = 2 \times \angle SPQ$ and $\angle SPQ = 2 \times \angle PQR$ . Also $\angle QRS = k \times \angle PQR$ . What is the value of $k$ ?

(A) $2$ (B) $3$ (C) $4$ (D) $5$ (E) $6$

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.