Question

measure of each angle.
\\( \angle u v w \\) and \\( \angle x y z \\) are complementary angles, \\( m \angle u v w = ( x - 10 ) ^ { \circ } \\), and \\( m \angle x y z = ( 4 x - 10 ) ^ { \circ } \\).
\\( m \angle u v w = \square ^ { \circ } \\)
\\( m \angle x y z = \square ^ { \circ } \\)

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((x - 10)+(4x - 10)=90\).

Step2: Simplify the equation

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 \(5x=110\). Then divide by \(5\): \(x=\frac{110}{5}=22\).

Step4: Find \(m\angle UVW\)

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

Step5: 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:

\(m\angle UVW = 12^{\circ}\), \(m\angle XYZ=78^{\circ}\)