Library / UKMT Junior Mathematical Olympiad /85 of 98

UKMT Junior Mathematical Olympiad, 2016

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In a certain triangle, the size of each of the angles is a whole number of degrees. Also, one angle is $30°$ larger than the average of the other two angles. What is the largest possible size of an angle in this triangle?

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.