Question

question 37 module 7 practice test
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in the triangle below, with right angle ∠w, suppose that $m∠v=(5x - 18)°$ and $m∠x=(4x - 27)°$.
find the degree measure of each angle in the triangle.
$m∠v=\square°$
$m∠w=\square°$
$m∠x=\square°$

Explanation:

Step1: Sum of acute angles = 90°

The triangle is right-angled at $W$, so the sum of $\angle V$ and $\angle X$ is $90^\circ$.
$$(5x - 18) + (4x - 27) = 90$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$9x - 45 = 90$$
$$9x = 135$$
$$x = 15$$

Step3: Calculate $m\angle V$

Substitute $x=15$ into the expression for $\angle V$.
$$m\angle V = 5(15) - 18 = 75 - 18 = 57$$

Step4: Calculate $m\angle X$

Substitute $x=15$ into the expression for $\angle X$.
$$m\angle X = 4(15) - 27 = 60 - 27 = 33$$

Step5: Identify $m\angle W$

$\angle W$ is the right angle, so its measure is $90^\circ$.

Answer:

$m\angle V = 57^\circ$
$m\angle W = 90^\circ$
$m\angle X = 33^\circ$