In the Following Figures, Find the Remaining Angles of the Parallelogram

Question

In the following figures, find the remaining angles of the parallelogram

Sum

Solution

ABCD is a parallelogram.
∠A = 75°
⇒ ∠C = 75° ....(Opposite angles of a parallelogram are eequal)
Now,∠A + ∠D = 180° ....(Interior angles)
⇒ ∠75° + ∠D = 180°
⇒ ∠D = 105°
⇒ ∠B = ∠D = 105° ....(Opposite angles of a parallelogram are equal)
Thus, we have
∠B = 105°, ∠C = 75° and ∠D = 105°.

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Properties of a Parallelogram - Property: The Opposite Angles of a Parallelogram Are of Equal Measure.

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