Question

find the measure of each angle.
∠uvw and ∠xyz are complementary angles, m∠uvw=(x - 10)°, and m∠xyz=(4x - 10)°.
m∠uvw=□°
m∠xyz=□°

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90°. So, $(x - 10)+(4x - 10)=90$.

Step2: Combine like - terms

$x+4x-10 - 10 = 90$, which simplifies to $5x-20 = 90$.

Step3: Add 20 to both sides

$5x-20 + 20=90 + 20$, resulting in $5x=110$.

Step4: Solve for x

Divide both sides by 5: $x=\frac{110}{5}=22$.

Step5: Find $m\angle{UVW}$

Substitute $x = 22$ into $m\angle{UVW}=(x - 10)^{\circ}$. So, $m\angle{UVW}=(22 - 10)^{\circ}=12^{\circ}$.

Step6: Find $m\angle{XYZ}$

Substitute $x = 22$ into $m\angle{XYZ}=(4x - 10)^{\circ}$. So, $m\angle{XYZ}=(4\times22 - 10)^{\circ}=(88 - 10)^{\circ}=78^{\circ}$.

Answer:

$m\angle{UVW}=12$
$m\angle{XYZ}=78$