Question

Determine x,y, and z.

80°
100°
55°
60°
The measure ofx is
The measure of y is
The measure of z is

Answer 1

Answer: x = 20

y = 45

z = 115

Explanation:

There is one unknown variable in both triangles with known angles. To find the values of x, y, and z, add both the known angles and subract it from 180 degrees. The result will be the value of the variable. When you have both the values of x and y, do the same math to find the value of z.

Step 1: Find the value of x

Add the values of the two known angles in this traingle and subtract it from 180°

80 + 55 = 135

180 - 135 = 45

45° is the value of x

Step 2: Find the value of y

Add the values of the two known angles in this traingle and subtract it from 180°

100 + 60 = 160

180 - 160 = 20

20° is the value of y

Step 3: Find the values of z

Add the values of x and y and subtract it from 180°

45 + 20 = 65

180 - 65 = 115

115° is the value of z

Answer 2

Explanation:

You can get y and x immediately. z is a bit tricky.

x

The other two angles of a triangle containing x are 100 and 60.

x + 100 + 60 = 180 Add the two terms on the left

x + 160 = 180 Subtract 160 from 180

x = 180 - 160 Combine the right

x = 20

y

y is done exactly the same way.

55 + 80 + y = 180

135 + y = 180

y = 180 - 135

y = 45

z

You have x y and z all in the same triangle. You know x and y so z can be found in much the same way.

x + y + z = 180

20 + 45 + z = 180

65 + z = 180

z = 180 - 65

z = 115