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CEMC Gauss (Grade 8), 2023

Geometry Difficulty 2.4 Junior Find the answer Canada

The diagram is made up of four congruent rectangles with
dimensions 3 by 4.

What is the length of the path from $A$ to $B$ shown on the diagram?

Pick one

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 $\angle ABC=180\degree-105\degree-35\degree=40\degree$ .

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