Question

the figure shows two parallel lines intersected by two transversals. two of the angle measurements are given. find the measures of angles 1, 2, and 3.
the measure of angle 1 is 60° . (simplify your answer.)
the measure of angle 2 is □° . (simplify your answer.)

Explanation:

Step1: Use the property of supplementary angles

Since angle 1 and angle 2 are supplementary (they form a linear - pair), the sum of their measures is \(180^{\circ}\). Let \(m\angle1 = 60^{\circ}\) and \(m\angle2=x\). Then the equation is \(m\angle1 + m\angle2=180^{\circ}\).

Step2: Solve the equation for \(m\angle2\)

Substitute \(m\angle1 = 60^{\circ}\) into the equation \(60^{\circ}+x = 180^{\circ}\).
Subtract \(60^{\circ}\) from both sides: \(x=180^{\circ}-60^{\circ}\).

Answer:

\(120\)