Library / CEMC Gauss (Grade 7) /209 of 462

CEMC Gauss (Grade 7), 2012

Geometry Difficulty 1.2 Junior Find the answer Canada

Two straight lines intersect as shown.

The measure of the angle marked $\Box$ is

Pick one

Solution

Solution 1

The angle marked $\Box$ is vertically opposite the angle measuring $60\degree$ .

Since vertically opposite angles are equal, then the measure of the angle marked $\Box$ is also $60\degree$ .

Solution 2

The measure of a straight angle is $180\degree$ .

Together, the angle measuring $120\degree$ and the angle marked $\Box$ make up a straight angle.

That is, $120\degree + \Box = 180\degree$ .
Therefore, the angle marked $\Box$ is $60\degree$ .

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.