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Problem 384

Geometry Difficulty 2.1 Find the answer CEMC Fermat · Canada · 2012

In the diagram, $HF=HG$ and $JFG$ is a straight line segment. The value of $x$ is

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Since $JFG$ is a straight line, then $\angle HFG = 180^\circ - \angle HFJ = 180^\circ - 110^\circ = 70^\circ$ .

Since $\triangle FGH$ is isosceles with $HF = HG$ , then $\angle HGF = \angle HFG = 70^\circ$ .

Since the sum of the angles in $\triangle FGH$ is $180^\circ$ , then $70^\circ + 70^\circ + x^\circ = 180^\circ$ , and so $140+x = 180$ or $x=40$ .

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