Problem 1
Angles A and B are adjacent in parallelogram ABCD. For any parallelogram, adjacent angles are supplementary.
A+B = 180
2x+(x+6) = 180
3x+6 = 180
3x = 180-6
3x = 174
x = 174/3
x = 58
Use this x value to find angles A and B
angle A = 2x = 2*58 = 116 degrees
angle B = x+6 = 58+6 = 64 degrees
Answer: 64 degrees
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Problem 2
Let y be the measure of the unknown angle that's supplementary to the 42 degree angle. This must mean that,
y+42 = 180
y = 180-42
y = 138 degrees
Answer: D) 138 degrees
The measure of ∠B is 64 degrees.
The angle that is supplement ot the angle 42 degrees is 138 degrees.
Supplementary angles are angles that sum up to 180 degrees. When two angles sum up to 180 degrees, they are supplementary angles.
Therefore,
Adjacent angles of a parallelograms are supplementary.
Hence,
∠A + ∠B = 180
2x + x + 6 = 180
3x + 6 = 180
3x = 180 - 6
3x = 174
x = 174 / 3
x = 58
Therefore,
∠B = 58 + 6 = 64°
The other angle that is supplement to 42 degrees is as follows;
42 + y = 180
y = 180 - 42
y = 138°
learn more on supplementary angles here:https://brainly.com/question/13045673
