Question

The diagonal AC and BD of a parallelogram ABCD intersect each other at point O.If angle DAC=30° and angle AOB=70°,then what is the measure of angle DBC?

Answer 1

Answer:

Draw the picture. I'm not smart enough to do it without being able to look at it.

If angle AOB = 70, the opposite angle, DOC, is also 70. These two angles total 140, so the othe two central angles, BOC and AOD, total 220 (360 - 140), and each one = 110. Since angle DAC = 32, angle ACB also = 32. All the interior angles of a triangle = 180. Adding the two known angles (BOC = 110, OCB = 32) = 142. Subtracting 142 from 180 = 32.

Angle DBC = 32.

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