ABCD is a rhombus where angle DAB = 140 degrees. AE is drawn such that AE bisects angle DAB and E is a point on BC. Find angle AEB.
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Worked Solution
Step 1: Find angle ABC using the property of a rhombus.
In a rhombus, AD is parallel to BC, so angle DAB and angle ABC are co-interior angles.
Angle ABC = 180 - 140 = 40 degrees
Step 2: Find angle BAE using the angle bisector.
AE bisects angle DAB, so angle BAE = 140 / 2 = 70 degrees
Step 3: Find angle AEB using the angle sum of triangle ABE.
Angle AEB = 180 - angle BAE - angle ABE
Angle AEB = 180 - 70 - 40 = 70 degrees
Answer: Angle AEB = 70 degrees
Correct answer: 70°
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