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# Triangles: Isosceles

In the figure below, what is the value of $$x^\circ$$? ![](data:image/svg+xml;base64,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)
Correct. [[snippet]] Given that $$AC = BC$$, >$$\displaystyle{\angle CAB = \angle CBA = \frac{180^\circ - 100^\circ}{2} = 40^\circ}$$. Since $$\angle CAB$$ and $$x^\circ$$ are supplementary angles, >$$x^\circ = 180^\circ - 40^\circ = 140^\circ$$.
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
40º
65º
100º
115º
140º