First, we need to get angle 1 on the same transversal as angle 2.
1.) By the alternate exterior angles theorem, the angle at the intersection of DH is 60°.
2.) By the same theorem, m∠1 is equal to the measure of the angle at GD.
3.) Line GH is a straight line, meaning it has an angle measure of 180°. So, we can create the equation: m∠1+60°=180°. Now, we solve for m∠1, so we will subtract 60 from both sides. m∠1=180-60 ———> m∠1=120.
4.) Now, by the corresponding angles theorem, angle 1 is equal to angle 2. We now know that m∠1=120°, which means m∠2=120°.
5.) So, we need to find: m∠1+m∠2. Substitute the angle measures in for both angles (remember, they are equal, so they will have the same angle measure). (120)+120)=240. So, your answer is 240°.