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?
A.
x = 18; m∠XOY = 6°
B.
x = 20; m∠XOY = 6°
C.
x = 6; m∠XOY = 18°
D.
x = 6; m∠XOY = 20°
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Answer 1

To find the value of x and m∠XOY, we need to use the properties of supplementary and complementary angles.

1. ∠WOZ and ∠WOX are supplementary angles:
This means that the sum of the two angles is 180 degrees.
∠WOZ + ∠WOX = 180

2. ∠WOX and ∠XOY are complementary angles:
This means that the sum of the two angles is 90 degrees.
∠WOX + ∠XOY = 90

From the second equation, we can substitute ∠WOX as (180 - ∠WOZ):
(180 - ∠WOZ) + ∠XOY = 90
180 - ∠WOZ + ∠XOY = 90
∠XOY = ∠WOZ - 90

Now we substitute this into the first equation:
∠WOZ + (180 - ∠WOZ) = 180
180 = 180
This equation is always true, but we need it to solve for x and m∠XOY.

Since the equation is always true, there are multiple possible solutions. Therefore, we need to choose one based on the answer choices provided.

From the answer choices, we can see that x is either 6 or 20. Let's try x = 6:

If x = 6, then m∠WOX = 6 and m∠WOZ = 174
Now we can find m∠XOY = m∠WOZ - 90 = 174 - 90 = 84

Therefore, x = 6 and m∠XOY = 84.

So, the correct answer is:
C. x = 6; m∠XOY = 84°.