Question

For the following diagram, assume that

L || M
.



Solve for each of the variables,
x
and
y
. For each solution, use complete sentences to explain which special angles allowed you to create an equation in order to find the solution.

Answer 1

Answer: x=80

Y=15

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Answer 2

x = 80

y = 15

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