Library / UKMT Intermediate Mathematical Challenge /258 of 267

UKMT Intermediate Mathematical Challenge, 2017

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

The diagram shows two rectangles and a regular pentagon. One side of each rectangle has been extended to meet at $X$ . What is the value of $x$ ?

(A) $52$ (B) $54$ (C) $56$ (D) $58$ (E) $60$

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.