Answer:
x = 65°
y = 15°
z = 149°
Explanation:
A triangle's interior angles all add up to have a sum of 180 degrees.
Given in the triangle with two angle measures already given, we can infer that the third angle, x, is equal to 65 degrees.
Set up an equation to say that the two angles plus the unknown angle is equal to 180 degrees:
35 + 80 + x = 180
Combine like terms:
115 + x = 180
Subtract because the inverse operation of addition is subtraction:
-115 -115
x = 65°
Supplementary angles which can be composed of only 2 angles have a sum of 180 degrees and form a straight angle.
Now that we know x is equal to 65 degrees, we can infer that it is supplementary to angle y as they both form a straight angle.
Set up an equation saying that the angle x (65 degrees) and angle y (our unknown value that we're trying to solve for) have a sum of 180 degrees:
65 + y = 180
Subtract because inverse operation of addition is subtraction:
-65 -65
y = 15°
Using our knowledge that the sum of the three interior angles of a triangle have a sum of 180 degrees, we can set up an equation similar to the first one saying that the two angles given (one of which we have found to be equal to 15 degrees, angle y) plus the unknown angle have a sum of 180 degrees:
16 + 15 + z = 180
Combine like terms:
31 + z = 180
Inverse operation of addition is subtraction:
-31 -31
z = 149°
You can also double check that these values are correct by adding these angles' values that we've found out plus the given values and see if they equal to 180 degrees in these two separate triangles:
35 + 80 + 65 = 180
180 = 180, x is correct.
16 + 15 + 149 = 180
180 = 180, y and z are correct.