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Triangles: Isosceles

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) If $$AB=BC$$, $$DA=AC$$, and angles $$DCB$$ and $$ABC$$ are right angles as shown above, then what is the value of $$x^\circ$$?
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Correct. [[snippet]] Since triangle $$ABC$$ is a right isosceles triangle, you know that >$$\displaystyle{\angle BAC =\angle BCA = 45^\circ}$$. Based on this, >$$\angle ACD = 90^\circ - 45^\circ = 45^\circ$$. Given that $$AD = AC$$, you know that $$\angle ADC = \angle ACD = 45^\circ$$. Hence, >$$x^\circ = 180^\circ - 2(45^\circ) = 90^\circ$$.
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