SOLUTION: Given ABCD is a parallelogram, angle A= (x+6)degrees, and angle B= (2x+15)degrees,then find the measure of angle D. A) 21 B) 127 C) 53 D) 121

Question 557284: Given ABCD is a parallelogram, angle A= (x+6)degrees, and angle B= (2x+15)degrees,then find the measure of angle D.
A) 21
B) 127
C) 53
D) 121
Answer by heilok(4) (Show Source): You can put this solution on YOUR website!
Hi,

Here are a few reminders about solving the problem:
1) angle sum of parallelogram=360 degrees
2) opposite angles of parallelogram are equal in size
3) sum of interior angles of parallelogram=180 degree

Very unfortunately, the question didn't tell you whether angle A and angle B are a pair of opposite angles or interior angles. So you need to try it out yourself.

Firstly, assume angle A and angle B are a pair of opposite angles. Therefore,

x+6=2x+15
2x-x=6-15
x=-9.

However, let's calculate the size of angle A in this case.

Sub x=-9,
angle A=x+6
=-9+6
=-3 ,which is impossible to be an angle.
Now ,the conclusion is: angle A and angle B are a pair of interior angles. Therefore,
(x+6)+(2x+15)=180
3x=180-21
x=53

so,angle A=x+6
=59.

If angle A and angle D are a pair of opposite angles,
Therefore angle A=Angle D
Angle D=x+6
=53+6
=59

If angle A and angle D are a pair of interior angles,

Therefore angle A+Angle D =180
59+angle D = 180
Angle D=121

Angle D can be 59 or 121 degrees.
Ans. D

Cheers,
Heil
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