Question

Given parallelogram ABCD, angle D = 2x + 25, and angle B = 3x + 6, find angle A. (Please note, canvas is broken so I had to rewrite it.)

Answer 1

Opposite angles in a parallelogram have the same measure, then we can formulate the following expression for angles D and B:

m2x + 25 = 3x + 6

From this equation, we can solve for x to get:

2x = 3x + 6 - 25

2x = 3x - 19

2x - 3x = -19

-x = -19

x = 19

Now that we have the value of x we can replace it into the measure of angle B to get:

m

m

Angles A and B are supplementary, that is their measures sum up to 180°, then we can formulate the following equation:

mmmm

Then, the measure of angle A equals 117°