Question

If ∠WOZ and ∠WOX are supplementary angles and ∠WOX and ∠XOY are complementary angles, then what is the value of x and m∠XOY?

Answer 1

Since ∠WOX and ∠XOY are complementary angles, their sum is 90 degrees. Therefore, x = 90 - m∠WOX

Since ∠WOZ and ∠WOX are supplementary angles, their sum is 180 degrees. Therefore, m∠WOX + m∠WOZ = 180.

We know that m∠WOX + m∠XOY = 90. Substituting the first equation in this equation, we get:

(180 - m∠WOX) + m∠XOY = 90
180 - m∠WOX + m∠XOY = 90
Subtracting 180 from both sides:
-m∠WOX + m∠XOY = -90
Rearranging the terms:
m∠XOY = -90 + m∠WOX

So, x = 90 - m∠WOX
x = 90 - (180 - m∠WOX)
x = -90 + m∠WOX

In conclusion:
x = -90 + m∠WOX
m∠XOY = -90 + m∠WOX.