Answer:
1. x = 120°
2. x = 115°
Step-by-step explanation:
For the first question, you can see that the two lines are parallel. This means you can use any of the alternate interior angles, alternate exterior angles, corresponding angles, consecutive interior angles, and consecutive exterior angles.
You can see that the transversal cutting the two parallel lines make a 40° angle, and through alternate interior angles, the angle next to x is also 40°.
Because a straight line is 180°, the three angles that make up the straight line will add up to 180°. So:
x + 20° + 40° = 180°
x + 60° = 180°
x = 120°
For the second question, extend the line (the left one marked with 1 arrow) to make a smaller triangle attached to the parallelogram.
Because this is a parallelogram, opposite angles are congruent. So the opposite angle of x is also x.
Straight lines are 180°, so 180 - x will be what the angle measure is. If this is too confusing, refer to the image below.
Those two angles, 50° and (180 - x)°, will add up to be the exterior angle, which is also x.
So:
50 + 180 - x = x
230 = 2x
115 = x
x = 115
