In parallelogram ABCD given below:If ∠B=40°, then find the value of ∠A,∠Cand∠D.
A
∠A=140°,∠C=40°and∠D=40°
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B
∠A=140°,∠C=40°and∠D=140°
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C
∠A=40°,∠C=40°and∠D=140°
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D
∠A=140°,∠C=140°and∠D=40°
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Solution
The correct option is D∠A=140°,∠C=140°and∠D=40° In this figure,
Given that, ∠B=40°.
We know that the opposite angles of a parallelogram are equal.
So, ∠B=∠D ∴∠D=40°
The sum of consecutive angles of a parallelogram is equal to 180°.
As, ∠B and ∠C are consecutive angles, ∴∠B+∠C=180° ⇒40°+∠C=180° ⇒∠C=180°−40°=140° ∠Cand∠A are opposite angles, ∴∠C=∠A=140°