Question

in $delta wxy$, $overline{wy}$ is extended through point $y$ to point $z$, $mangle ywx=(2x + 9)^{circ}$, $mangle wxy=(2x + 16)^{circ}$, and $mangle xyz=(8x + 1)^{circ}$. find $mangle wxy$.

Explanation:

Step1: Use the exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle WXY\), \(\angle XYZ\) is an exterior angle, so \(m\angle XYZ=m\angle YWX + m\angle WXY\).
Substitute the given angle expressions: \((8x + 1)=(2x + 9)+(2x + 16)\).

Step2: Simplify the right - hand side of the equation

\((2x + 9)+(2x + 16)=2x+2x + 9 + 16=4x+25\). So the equation becomes \(8x + 1=4x + 25\).

Step3: Solve for \(x\)

Subtract \(4x\) from both sides: \(8x-4x + 1=4x-4x + 25\), which simplifies to \(4x+1 = 25\).
Then subtract 1 from both sides: \(4x+1 - 1=25 - 1\), getting \(4x=24\).
Divide both sides by 4: \(x = 6\).

Step4: Find \(m\angle WXY\)

Substitute \(x = 6\) into the expression for \(m\angle WXY\). Since \(m\angle WXY=(2x + 16)^{\circ}\), then \(m\angle WXY=2\times6+16=12 + 16=28^{\circ}\).

Answer:

\(28^{\circ}\)