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Problem 237

Geometry Difficulty 1.4 Multiple choice CEMC Gauss (Grade 7) · Canada · 2023

In the diagram, $BCD$ is a
straight line segment.

The measure of $\angle ABC$ is

Pick one

Official solution

Since $BCD$ is a straight line
segment, then $\angle BCD =180\degree$ .

Therefore, $\angle ACB =\angle BCD-\angle ACD=180\degree-75\degree=105\degree$ .

Since the sum of the three angles in $\triangle ABC$ is $180\degree$ , then $\angle ABC=180\degree-105\degree-35\degree=40\degree$ .

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