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In parallelogram ABCD, BAD = 110^. E is a point on AD such that AE = AB. Calculate CED.

Mathematics

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Part 3

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Calculate ∠CED\angle CED

  1. Identify properties of the parallelogram ABCD.

    In a parallelogram, opposite sides are equal and consecutive angles are supplementary.
    Given ∠BAD=110∘\angle BAD = 110^\circ.
    Since E is on AD, ∠BAE=∠BAD=110∘\angle BAE = \angle BAD = 110^\circ.

  2. Analyze △ABE\triangle ABE.

    We are given that AE=ABAE = AB. Since AB=50AB = 50 mm, then AE=50AE = 50 mm.
    Because AE=ABAE = AB, △ABE\triangle ABE is an isosceles triangle.
    The base angles of an isosceles triangle are equal

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