Question

if m∠wxz=(5x + 3)°, m∠zxy=(8x - 4)° and ∠wxy is a right angle, find m∠zxy

Explanation:

Step1: Use angle - addition postulate

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

Step2: Combine like - terms

$5x+8x+3 - 4=90$, which simplifies to $13x-1 = 90$.

Step3: Solve for $x$

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

Step4: Find $m\angle ZXY$

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

Answer:

$52^{\circ}$