In parallelogram ABCD, A = 4x + 8 and C = 6x –10. Find the measure of A .

Explanation

Parallelogram ABCD describes a parallelogram with its 4 angles named as A,B,C and D . A is opposite C, and B is opposite D . Opposite angles in parallelograms are equal in measure. Hence,
The measure of A = C, and the measure of B = D.
Given the equations for A and C, we can set them as:
A = C
4x + 8 = 6x - 10
8 + 10 = 6x – 4x
18 = 2x
x = 18/2 = 9
Computing for the measure of A:
A = 4x + 8 = 4(9) + 8 = 36 + 8 = 44 degrees

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