Answers:
- M = 128
- N = 128
- O = 52
- P = 52
Explanation
The tick marks tell us that we have an isosceles trapezoid. That will mean the angles marked are congruent.
angle M = angle N
8x-16 = 6x+20
8x-6x = 20+16
2x = 36
x = 36/2
x = 18
Let's use that to find the following angles.
- angle M = 8x-16 = 8*18-16 = 128
- angle N = 6x+20 = 6*18+20 = 128
We the same result each time to confirm we have the correct value of x.
Angles M and P are supplementary due to the parallel lines. These are same side interior angles, aka consecutive interior angles.
M+P = 180
128+P = 180
P = 180-128
P = 52
This is also the measure of angle O for similar reasoning.
Side note: The four angles add to 360 degrees. This applies to any quadrilateral.
