Question

1. if (mangle wxz=(5x + 3)^{circ}), (mangle zxy=(8x - 4)^{circ}), and (angle wxy) is a right - angle, find each measure.

Explanation:

Step1: Use angle - addition postulate

Since $\angle WXY$ is a right - angle ($m\angle WXY = 90^{\circ}$) and $\angle WXY=\angle WXZ+\angle ZXY$, we have the equation $(5x + 3)+(8x-4)=90$.

Step2: Combine like terms

Combining the $x$ terms and the constant terms on the left - hand side of the equation, we get $(5x+8x)+(3 - 4)=90$, which simplifies to $13x-1 = 90$.

Step3: Solve for $x$

Add 1 to both sides of the equation: $13x-1 + 1=90 + 1$, so $13x=91$. Then divide both sides by 13: $x=\frac{91}{13}=7$.

Step4: Find $m\angle WXZ$

Substitute $x = 7$ into the expression for $m\angle WXZ$: $m\angle WXZ=5x + 3=5\times7+3=35 + 3=38^{\circ}$.

Step5: Find $m\angle ZXY$

Substitute $x = 7$ into the expression for $m\angle ZXY$: $m\angle ZXY=8x-4=8\times7-4=56 - 4=52^{\circ}$.

Answer:

$x = 7$
$m\angle WXZ=38^{\circ}$
$m\angle ZXY = 52^{\circ}$