3340.12 – Trapezoid Angle Measure

The figure below, not drawn to scale, shows a trapezoid, ABCDABCD with AB∥CD AB \parallel CD. The diagonal BDBD is drawn and BD=AD,∠DCB=110BD =AD, \angle DCB = 110 degrees, and ∠CBD=30\angle CBD = 30 degrees. What is ∠ADB\angle ADB?

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Solution

Using co-interior angles, 110+30+∠B1=180. 110 + 30 + \angle B1 = 180. Then,

∠D1=B1=40,\angle D1 = B1 = 40,

∠A=40,\angle A = 40,

∴∠D2=100.\therefore \angle D2 = 100.

That's the answer: 100 degrees.

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