Question

in figure $overline{ab}$ is parallel to $overline{cd}$ and $overline{ef}$ is parallel to $overline{gh}$. find the sum of $angle1$ and $angle2$. note: use ctrl - d to drag the option via keyboard. sum of $angle1$ and $angle2$ is

Explanation:

Step1: Use property of parallel lines

Since \(AB\parallel CD\) and \(EF\parallel GH\), \(\angle 1\) and the angle adjacent to the \(60^{\circ}\) angle on line \(CD\) are corresponding - angles. The angle adjacent to the \(60^{\circ}\) angle on line \(CD\) is \(120^{\circ}\) (linear - pair: \(180 - 60=120^{\circ}\)), so \(\angle 1 = 120^{\circ}\).

Step2: Use property of parallel lines for \(\angle 2\)

\(\angle 2\) and the \(60^{\circ}\) angle are corresponding angles. So \(\angle 2=60^{\circ}\).

Step3: Calculate the sum

\(\angle 1+\angle 2=120^{\circ}+60^{\circ}=180^{\circ}\)

Answer:

\(180^{\circ}\)