A quadrilateral in which opposite sides are parallel is called a parallelogram. The measure of the ∠C is 138°.
What is a parallelogram?
A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a quadrilateral to be a parallelogram the pair of opposite sides should be equal and parallel. Also, the measure of the opposite angles should be equal. Therefore, the measure of the opposite sides can be written as,
∠B = ∠D = 42°
And, ∠A = ∠C
Since the sum of all the angles of a quadrilateral is 360°. Therefore, the sum of all the angles can be written as,
∠A + ∠B + ∠C + ∠D = 360°
∠C + 42° + ∠C + 42° = 360°
2∠C = 276°
∠C = 138°
Hence, the measure of the ∠C is 138°.
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