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: Use complementary - angle property

Since $\angle UVW$ and $\angle XYZ$ are complementary, $m\angle UVW + m\angle XYZ=90^{\circ}$.
So, $(x - 10)+(4x - 10)=90$.

Step2: Simplify the left - hand side

Combine like terms: $x+4x-10 - 10 = 90$, which gives $5x-20 = 90$.

Step3: Solve for $x$

Add 20 to both sides: $5x=90 + 20$, so $5x=110$.
Divide both sides by 5: $x=\frac{110}{5}=22$.

Step4: Find $m\angle UVW$

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

Step5: Find $m\angle XYZ$

Substitute $x = 22$ into $m\angle XYZ=(4x - 10)^{\circ}$.
$m\angle XYZ=(4\times22 - 10)^{\circ}=(88 - 10)^{\circ}=76^{\circ}$.

Answer:

$m\angle UVW = 14^{\circ}$, $m\angle XYZ = 76^{\circ}$