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# Lines & Angles: Perpendicular

In the figure below, what is the value of $$x$$? ![](data:image/svg+xml;base64,<?xml version="1.0" encoding="utf-8"?>
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</svg>
)
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Correct. [[snippet]] Since $$ABD$$ is an equilateral triangle, all three angles in this triangle are equal. >$$\angle ADB = \angle DBA = \angle BAD = \frac{180^\circ}{3} = 60^\circ$$. Based on this, >$$\angle BDC = 180^\circ - 70^\circ - 60^\circ = 50^\circ$$. Finally, the sum of all angles in a triangle is 180°, so >$$x = 180^\circ - 90^\circ - 50^\circ = 40^\circ$$.
Incorrect. [[snippet]]
Incorrect. [[snippet]] This is the measure of angle $$BDC$$.
30°
40°
50°
60°
70°