Question

find the value of the variable and the measure of each labeled angle.
points: 0 of 1
o points: 09.08%, 13.82 of 20 points

Explanation:

Step1: Set up the equation

Vertical - angles are equal. So, \(4x - 20=x + 15\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(4x - x-20=x - x + 15\), which simplifies to \(3x-20 = 15\). Then add 20 to both sides: \(3x-20 + 20=15 + 20\), getting \(3x=35\). Divide both sides by 3: \(x=\frac{35}{3}\). But if we assume these are supplementary - angles (since the question seems to be about angle - measures and we may have mis - identified the relationship), and they are linear pairs, then \((4x - 20)+(x + 15)=180\).

Step3: Expand and simplify the new equation

\(4x-20+x + 15=180\), combine like terms: \(5x-5 = 180\).

Step4: Solve the new equation for \(x\)

Add 5 to both sides: \(5x-5 + 5=180 + 5\), so \(5x=185\). Divide both sides by 5: \(x = 37\).

Step5: Find the measure of the angles

For the angle \(x + 15\), substitute \(x = 37\), we get \(37+15=52^{\circ}\). For the angle \(4x - 20\), substitute \(x = 37\), \(4\times37-20=148 - 20=128^{\circ}\).

Answer:

\(x = 37\)