CEMC Cayley, 2014

Geometry Difficulty 1.1 Junior Find the answer Canada

In the diagram, three line segments intersect as shown.

The value of $x$ is

Pick one

Solution

The unlabelled angle inside the triangle equals its vertically opposite angle, or $40^\circ$ .

Since the sum of the angles in a triangle is $180^\circ$ , then $40^\circ + 60^\circ + x^\circ = 180^\circ$ or $100+x=180$ .

Thus, $x=80$ .

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: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.