Asked by ashley
Trapezoid A B C D is shown. A diagonal is drawn from point B to point D. Sides B C and A D are parallel. Sides B A and C D are congruent. Angle C B D is 24 degrees and angle B A D is 116 degrees.
What is the measure of angle ABD in trapezoid ABCD?
24°
40°
64°
92°
All Answers 1
Answered by
GPT-5 mini
AI
92°
Reason: AB = CD makes the trapezoid isosceles, so base angles A and B are equal. Given ∠BAD = 116°, we have ∠ABC = 116°. The diagonal BD splits ∠ABC into ∠ABD and ∠CBD, and ∠CBD = 24°, so ∠ABD = 116° − 24° = 92°.
Reason: AB = CD makes the trapezoid isosceles, so base angles A and B are equal. Given ∠BAD = 116°, we have ∠ABC = 116°. The diagonal BD splits ∠ABC into ∠ABD and ∠CBD, and ∠CBD = 24°, so ∠ABD = 116° − 24° = 92°.
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