Question

current skill
find the measure of angle 6.

Explanation:

Step1: Use the property of supplementary angles

Since \(2x + 115\) and \(- 3x+60\) are supplementary angles, we have the equation \((2x + 115)+(-3x + 60)=180\).
Simplify the left - hand side: \(2x+115 - 3x + 60=-x + 175\).
So, \(-x+175 = 180\).
Subtract 175 from both sides: \(-x=180 - 175\), then \(-x = 5\), and \(x=-5\).

Step2: Find the measure of \(2x + 115\)

Substitute \(x =-5\) into \(2x + 115\).
\(2\times(-5)+115=-10 + 115=105\).

Step3: Use the property of corresponding angles

Angle \(6\) and \(2x + 115\) are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are equal.

Answer:

\(105^{\circ}\)