Question

parallel lines s and t are cut by a transversal, r, as shown. what is the measure of angle 1? 20° 42° 138° 160°

Explanation:

Step1: Use the property of alternate interior angles

Since lines \(s\) and \(t\) are parallel and cut by transversal \(r\), \((7x - 2)^{\circ}\) and \((6x + 18)^{\circ}\) are alternate interior angles. So \(7x-2=6x + 18\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides: \(7x-6x-2=6x-6x + 18\), which gives \(x-2=18\). Then add \(2\) to both sides: \(x=18 + 2=20\).

Step3: Find the measure of \((7x - 2)^{\circ}\)

Substitute \(x = 20\) into \(7x-2\): \(7\times20-2=140-2 = 138^{\circ}\).

Step4: Use the linear - pair relationship to find \(\angle1\)

Since \(\angle1\) and \((7x - 2)^{\circ}\) form a linear pair (sum to \(180^{\circ}\)), \(\angle1=180-(7x - 2)\). Substitute \(x = 20\): \(\angle1=180-138=42^{\circ}\).

Answer:

\(42^{\circ}\)