Question

For the following diagram, assume that

Answer 1

Answer:

x = 80

y = 15

Step-by-step explanation:

The angle 6y = 90 degrees, because it forms a straight angle with the right angle next to it. 6y and the right angle next to it are also called supplementary angles (added up = 180 degrees)

6y = 90

y =15

x and the angle underneath it are also supplementary angles. We know the angle under x = 100 degrees, because that angle and the one marked 100 degrees are corresponding angles.

x + 100 =180

x = 80

Another way to solve for x is to look at the quadrilateral formed by the lines P and Q with L and M. The interior angles of a quadrilateral add up to 360 degrees. We know 6y = 90 degrees, and the angle above is is also 90, because L&M are parallel and P is perpendicular to them.

360 - 90 - 90 - 100 = 80