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Find all the angles of a parallelogram if one angle is 80°.
Dear StudentFor a parallelogram ABCD, opposite angles are equal.So, the angles opposite to the given 80° angle will also be 80°.It is also known that the sum of angles of any quadrilateral = 360°.So, if ∠A = ∠C = 80° then,∠A + ∠B + ∠C + ∠D = 360°Also, ∠B = ∠DThus,80° + ∠B + 80° + ∠D = 360°Or, ∠B +∠ D = 200°Hence, ∠B = ∠D = 100°Now, all angles of the quadrilateral are found which are:∠A = 80°∠B = 100°∠C = 80°∠D = 100°Thanks
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