Question

22.
$20x + 11^{circ}$ $25x - 14^{circ}$
$x=___$
$mangle1=___$

Explanation:

Step1: Set up the equation

Since vertical - angles are equal, we set \(20x + 11=25x-14\).

Step2: Isolate the variable terms

Subtract \(20x\) from both sides: \(20x + 11-20x=25x-14 - 20x\), which simplifies to \(11 = 5x-14\).

Step3: Solve for \(x\)

Add 14 to both sides: \(11 + 14=5x-14 + 14\), so \(25 = 5x\). Then divide both sides by 5: \(x=\frac{25}{5}=5\).

Step4: Find the measure of angle 1

Substitute \(x = 5\) into the expression for one of the vertical - angles. Let's use \(20x + 11\). Then \(m\angle1=20\times5 + 11=100 + 11=111^{\circ}\).

Answer:

\(x = 5\)
\(m\angle1=111^{\circ}\)