Question

The following figure is not drawn to scale.

1) Using complete sentences, describe how angle relationships can be used to find the value of in this figure. Then, find the value of x, showing all of your work.
2) Using complete sentences, describe how angle relationships can be used to find the value of y in this figure. Then, find the value of y, showing all of your work.

Answer 1

1) The sum of all the angles in a triangle is always 180 degrees, so to find x, you can set up an equation with the provided angles and solve.

45+60+x=180

105+x=180

x=75

2. x degrees and y degrees add up to 180 degrees, because they form a straight angle, which is a straight line. You can set up an equation using the value of x you found in the previous part and solve for y.

x+y=180

75+y=180

y=105