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Problem 52

Geometry Difficulty 1.2 Multiple choice CEMC Gauss (Grade 7) · Canada · 2012

Two straight lines intersect as shown.

The measure of the angle marked $\Box$ is

Pick one

Official 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 $60\degree$ .

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