Question

m∠WYX = (4x − 8)° and m∠WYZ = 10x°. If ∠WYX and ∠WYZ are complementary, find the measure of each angle.

Answer 1

The answers would be:
WYX = 20 degrees
WYZ = 70 degrees

Answer 2

Answer:

$m\angle WYX=20^{\circ}$

$m\angle WYZ=70^{\circ}$

Step-by-step explanation:

We have been given that $m\angle WYX=(4x-8)^{\circ}$ and $m\angle WYZ=(10x)^{\circ}$.

Since ∠WYX and ∠WYZ are complementary, so they will add up-to 90 degrees.

$m\angle WYZ+m\angle WYX=90^{\circ}$

Substitute the given values:

$4x-8+10x=90$

Combine like terms:

$14x-8=90$

$14x-8+8=90+8$

$14x=98$

$\frac{14x}{14}=\frac{98}{14}$

$x=7$

Let us substitute $x=7$ in measure of each angle as:

$m\angle WYX=(4(7)-8)^{\circ}$

$m\angle WYX=(28-8)^{\circ}$

$m\angle WYX=20^{\circ}$

Therefore, the measure of angle WYX is 20 degrees.

$m\angle WYZ=(10x)^{\circ}$

$m\angle WYZ=(10(7))^{\circ}$

$m\angle WYZ=70^{\circ}$

Therefore, the measure of angle WYZ is 70 degrees.