Question

1. for two vertical angles, (mangle a=(3x - 20)^{circ}) and (mangle b=(5x - 130)^{circ}). solve for (x), then find (mangle b). (x=square), (mangle b=square)

Explanation:

Step1: Set up equation

Since vertical - angles are equal, we set \(m\angle A=m\angle B\). So, \(3x - 20=5x-130\).

Step2: Solve for \(x\)

First, subtract \(3x\) from both sides: \(-20 = 5x-3x - 130\), which simplifies to \(-20=2x - 130\). Then add 130 to both sides: \(-20 + 130=2x\), so \(110 = 2x\). Divide both sides by 2: \(x=\frac{110}{2}=55\).

Step3: Find \(m\angle B\)

Substitute \(x = 55\) into the expression for \(m\angle B\). \(m\angle B=5x-130\), so \(m\angle B=5\times55 - 130=275-130 = 145\).

Answer:

\(x = 55\), \(m\angle B=145\)