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# Triangles: Isosceles

In isosceles triangle $$CEB$$ shown below, what is the value of $$x$$? ![](data:image/svg+xml;base64,<?xml version="1.0" encoding="utf-8"?>
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) _Note: Figure is not drawn to scale._
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Correct. [[snippet]] Since angles $$CEB$$ and $$AEB$$ are supplementary angles, >$$\angle CEB = 180^\circ - 100^\circ = 80^\circ$$. Based on this, you can find the measures of the angles that are equal in the isosceles triangle: >$$x = \frac{180^\circ - 80^\circ}{2} = 50^\circ$$.
Incorrect. [[snippet]]
40°
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