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Lines & Angles: Perpendicular

In the figure below, what is the value of $$x$$? ![](data:image/svg+xml;base64,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)
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Correct. [[snippet]] Angle $$ADC$$ is a supplementary angle of $$ADB$$, so $$\angle ADC = 90^\circ$$. Since the sum of all angles in a triangle is 180°, >$$x + 30^\circ + 90^\circ = 180^\circ$$ >$$x = 180^\circ - 90^\circ - 30^\circ = 60^\circ$$.
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