Question

1. solve for angle xyz.

Explanation:

Step1: Recall angle - sum property

The sum of angles on a straight - line is 180°. So, \(x + 4x+5x+(9x - 20)=180\).

Step2: Combine like - terms

\((x + 4x+5x+9x)-20 = 180\), which simplifies to \(19x-20 = 180\).

Step3: Isolate the variable term

Add 20 to both sides of the equation: \(19x-20 + 20=180 + 20\), resulting in \(19x=200\).

Step4: Solve for x

Divide both sides by 19: \(x=\frac{200}{19}\).

Step5: Find angle \(XYZ\)

Angle \(XYZ=x + 4x+5x=10x\). Substitute \(x = \frac{200}{19}\) into \(10x\), we get \(10\times\frac{200}{19}=\frac{2000}{19}\approx105.26^{\circ}\).

Answer:

\(\frac{2000}{19}\text{ degrees}\)