Question

level: basic
find the measure of angle 3.
label optional

Explanation:

Step1: Use the property of corresponding angles

Since \(2x + 75\) and \(6x-15\) are corresponding angles (assuming the two horizontal lines are parallel), we set them equal:
\(2x + 75=6x - 15\)

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(75 = 4x-15\)
Add \(15\) to both sides: \(90 = 4x\)
Divide by \(4\): \(x = 22.5\)

Step3: Find the measure of \(2x + 75\)

Substitute \(x = 22.5\) into \(2x + 75\): \(2\times22.5+75=45 + 75=120\)

Step4: Use the linear - pair relationship

Since angle \(1\) and \(2x + 75\) form a linear pair, angle \(1=180-(2x + 75)\). But angle \(3\) and \(2x + 75\) are vertical angles. Wait, no. Wait, angle \(1\) and \(2x + 75\) are adjacent and form a straight - line (\(180^{\circ}\)). But angle \(3\) and \(2x + 75\) are supplementary (linear pair). Wait, no, actually, if we consider the straight - line formed by the intersection of the transversal and the horizontal line. The angle \(2x + 75\) and angle \(3\) are supplementary (they form a linear pair).
Since \(2x+75 = 120\), then angle \(3=180 - 120\)

Answer:

\(60\)