Question

current skill show answer reque
7x + 40
1
4
3
6
5
8
-x + 72
find the measure of angle 4.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. Angle \(7x + 40\) and angle \(-x+72\) are vertical angles. So, \(7x + 40=-x + 72\).

Step2: Solve the equation for \(x\)

Add \(x\) to both sides: \(7x+x+40=-x+x + 72\), which simplifies to \(8x+40 = 72\).
Subtract \(40\) from both sides: \(8x+40-40=72 - 40\), so \(8x=32\).
Divide both sides by \(8\): \(x=\frac{32}{8}=4\).

Step3: Find the measure of angle \(7x + 40\)

Substitute \(x = 4\) into \(7x+40\): \(7\times4+40=28 + 40=68\).

Step4: Use the property of supplementary angles

Angle \(4\) and the angle \(7x + 40\) (\(68^{\circ}\)) are supplementary. So, \(\angle4=180-(7x + 40)\).
Substitute \(x = 4\): \(\angle4=180 - 68=112\).

Answer:

\(112\)