Question

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

( x=)
( mangle wxz=)
( mangle zxy=)

Explanation:

Step1: Set up the equation

Since \(\angle WXY\) is a right angle (\(90^{\circ}\)), \(m\angle WXZ + m\angle ZXY=90^{\circ}\). Substitute the given expressions: \((5x + 3)+(8x - 4)=90\).

Step2: Simplify the left - hand side

Combine like terms: \(5x+8x+3 - 4=90\), which simplifies to \(13x-1 = 90\).

Step3: Solve for \(x\)

Add \(1\) to both sides: \(13x=90 + 1=91\). Then divide both sides by \(13\): \(x=\frac{91}{13}=7\).

Step4: Find \(m\angle WXZ\)

Substitute \(x = 7\) into \(m\angle WXZ=(5x + 3)^{\circ}\). So \(m\angle WXZ=(5\times7+3)^{\circ}=(35 + 3)^{\circ}=38^{\circ}\).

Step5: Find \(m\angle ZXY\)

Substitute \(x = 7\) into \(m\angle ZXY=(8x - 4)^{\circ}\). So \(m\angle ZXY=(8\times7-4)^{\circ}=(56 - 4)^{\circ}=52^{\circ}\).

Answer:

\(x = 7\), \(m\angle WXZ = 38^{\circ}\), \(m\angle ZXY = 52^{\circ}\)