Question

Angles x, y, and z are angles. if x and y are complementary angles, x and z are supplementary angles, and y and z add up to 190, what is the value of z – x – y, in degrees?

Answer 1

If x and y are complimentary.....x + y = 90
if x and z are supplementary....x + z = 180
and y + z = 190

x + y = 90.....x = 90 - y

x + z = 180
90 - y + z = 180
z = 180 - 90 + y
z = 90 + y

y + z = 190
y + 90 + y = 190
2y + 90 = 190
2y = 190 - 90
2y = 100
y = 100/2
y = 50 <===

x = 90 - y
x = 90 - 50
x = 40 <===

z = 90 + y
z = 90 + 50
z = 140 <===

z - x - y = 140 - 40 - 50 = 50 <==