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Geometry Difficulty 2.6 Junior Find the answer Canada

Four of the angle measurements $\$62\degree, 85\degree, 99\degree, 108\degree, 114\degree\$$ are the measures of the angles in the same
quadrilateral. Which angle measure is not?

Pick one

Solution

The sum of the four angle measurements in a quadrilateral is
$360\degree$ .

The sum of the five angle measurements given is $62\degree+85\degree+99\degree+108\degree+114\degree=468\degree$ .

The difference, $468\degree-360\degree=108\degree$ , is the
measure of the angle that is not in the quadrilateral.

(We may confirm that $62\degree+85\degree+99\degree+114\degree=360\degree$ .)

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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.