Question

in the triangle below, ∠x is a right angle. suppose that ( mangle v=(5x - 39)^circ ) and ( mangle w=(3x + 17)^circ ).
(a) write an equation to find x. make sure you use an \=\ sign in your answer.
equation:
(b) find the degree measure of each angle.
( mangle v = ) (^circ)
( mangle w = ) (^circ)
( mangle x = ) (^circ)

Explanation:

Step1: Sum of acute angles = 90°

$(5x - 39) + (3x + 17) = 90$

Step2: Simplify left side

$8x - 22 = 90$

Step3: Solve for x

$8x = 112 \implies x = 14$

Step4: Calculate $m\angle V$

$m\angle V = 5(14) - 39 = 70 - 39 = 31$

Step5: Calculate $m\angle W$

$m\angle W = 3(14) + 17 = 42 + 17 = 59$

Step6: Identify $m\angle X$

Given as right angle: $m\angle X = 90$

Answer:

(a) Equation: $(5x - 39) + (3x + 17) = 90$
(b)
$m\angle V = 31^\circ$
$m\angle W = 59^\circ$
$m\angle X = 90^\circ$