# Ex 2B: Find the Measure of an Interior Angle of a Triangle

We want to find the measure of the missing angles. Looking at our diagram,

we want to determine the measure of angle x and

the measure of angle y. Notice in our diagram we

actually have three triangles. We have one smaller triangle here, another smaller triangle here, and then also a large triangle here. If we focus on the large

triangle, we can determine the measure of angle x

by using the fact that the sum of the interior

angles of any triangle is equal to 180 degrees. So again, focusing on the large triangle, the sum of this angle, this angle, and this angle must be 180 degrees. So writing an equation,

we would have x plus 56 plus, for this third angle,

we’d have the sum of 50 and 32, and the sum must equal 180. So solving for x, we’d have x plus 56, plus 50 plus 32 is

equal to 82, equals 180. Combining like terms, we

have x plus 56 plus 82 is equal to 138, and

finally, solving for x, we subtract 138 on both sides, giving us x equals 180 minus 138 is equal to 42. So if x equals 42, we now know the measure of this angle is 42 degrees. Now, let’s focus on this

upper smaller triangle. Notice how we have two of

the three interior angles, and therefore, we can now

determine the measure of angle y. So again, focusing on this

smaller upper triangle, or this green triangle, we

know the sum of this angle, this angle, and this angle

must measure 180 degrees. And therefore y plus 32

plus 42 must equal 180. So solving for y, we have y plus, well, 32 plus 42 is equal to 74, and then subtracting 74 on

both sides and simplifying, we have y equals 180

minus 74 is equal to 106. So if y is equal to 106, we know the measure of this angle is 106 degrees. And notice the unit of

degrees is already on x and y, so for our homework, we only enter x equals 42 and y equals 106. I hope you found this helpful.