Question

Refer to the figure below to complete the following problem.
The figure is parallelogram ABCD, which is a rhombus.
If the measure of Angle B is equal to 5x - 7 and the measure of Angle D is equal to 3x + 11, then what is the measure of Angle D?

A. 9 degrees
B. 17 degrees
C. 38 degrees
D. 77 degrees

Answer 1

A+D = 180°
So solve that for x, and you can then determine D.

Answer 2

I take the measure of Angle B and the measure of Angle D, and place the equal sign in between the two angles:
m∠B = m∠D
5x - 7 = 3x + 11
Then, I add 7 to the measure of angle B and the measure of angle D on both sides:
m∠B + 7 = m∠D + 7
5x - 7 + 7 = 3x + 11 + 7
Now, I can simplify. Since negative 7 and positive 7 equal 0, they cancel out:
5x = 3x + 18
Next, I subtract 3x to both sides of the simpified equation:
5x - 3x = 3x + 18 - 3x
After that, I simpify the equation the second time. Which will be simpified to:
2x = 18
Finally, I divide 2x and 18 by 2 and simpify.
2x/2 = 18/2
Since 2 divided by 2 equals 1, it will equal:
x = 18/2
After the equation is simpified, the answer would equal to:
x = 9
The equation would be:
m∠D = 3x + 11 = 3(9) + 11 = 38°
The answer is 38°.