n a quadrilateral ABCD, ⎳D is equal to 160° and ⎳A = ⎳B = ⎳C. Find ⎳A, ⎳B and ⎳C.
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Let ABCD be a parallelogram in which ∠A=65∘
.
Since AD∥BC we can treat AB as a transversal. So,
∠A+∠B=180 ∘
65 ∘ +∠B=180∘
∠B=180 ∘ −65∘
∠B=115∘
Since the opposite angles of a parallelogram are equal, we have
∠C=∠A=65 ∘and ∠D=∠B=115 ∘
Hence, ∠B=115 ∘
,∠C=65 ∘and ∠D=115 ∘
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