We know that m∠1 is 110°. If we look at m∠7 closely, we can see that while m∠1 is an obtuse angle (greater than 90° but less than 180°), m∠7 is an acute angle (less than 90°).
Now, we can eliminate 110° and 180° since we know that m∠7 is an acute angle. There are only 2 choices now: 40° or 70°.
If you flip the image around, you can see that the angle is slightly less than 90°, so it has to be 70°.
