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Problem 227

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

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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

Figure for this problem $\triangle$ ABC $is$ $180\degree$ $, then$ $\angle ABC=180\degree-105\degree-35\degree=40\degree\$.$

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