Question

7 find the measure of each angle.$angle uvw$ and $angle xyz$ are complementary angles,$mangle uvw = (x - 10)^circ$, and $mangle xyz = (4x - 10)^circ$.find $mangle uvw$ and $mangle xyz$.$mangle uvw = square^circ$$mangle xyz = square^circ$

Explanation:

Step1: Define complementary angles sum

Complementary angles sum to $90^\circ$.
$$(x-10) + (4x-10) = 90$$

Step2: Simplify the equation

Combine like terms and solve for $x$.
$$5x - 20 = 90$$
$$5x = 110$$
$$x = 22$$

Step3: Calculate $m\angle UVW$

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

Step4: Calculate $m\angle XYZ$

Substitute $x=22$ into $(4x-10)$.
$$m\angle XYZ = 4(22) - 10 = 88 - 10 = 78$$

Answer:

$m\angle UVW = 12^\circ$
$m\angle XYZ = 78^\circ$