Question

pre-algebra ic sem 2 fall 2025
geometry basics
parallel lines s and t are cut by a transversal, r, as
shown.
what is the measure of ∠1?
160°
20°
138°
42°

Explanation:

Step1: Use the property of alternate interior angles

Since \( t\parallel s \), the angles \((6x + 18)^{\circ}\) and \((7x-2)^{\circ}\) are equal. So we have the equation \(6x + 18=7x - 2\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides: \(18=x - 2\). Then add \(2\) to both sides: \(x=20\).

Step3: Find the measure of \(\angle1\)

Use the linear - pair property (the sum of adjacent angles on a straight line is \(180^{\circ}\)). Let's first find the measure of the angle \((6x + 18)^{\circ}\) (or \((7x - 2)^{\circ}\)). Substitute \(x = 20\) into \((6x+18)^{\circ}\), we get \(6\times20 + 18=120+18 = 138^{\circ}\). Then \(\angle1=180-(6x + 18)\) (or \(180-(7x - 2)\)). Substitute \(x = 20\) into \(180-(6x + 18)\), we have \(180-138 = 42^{\circ}\).

Answer:

\(42^{\circ}\)