m∠C = 60°
Here's why: The sum of the interior angles of a triangle is equal to 180°. We know one of the angles is 30°, and the other is 90°, as shown by the box in the corner. Added together, that equals 120°. Subtract 120° from 180°, and you get 60°.
m∠ABD = 55°
Here's why: Again, the sum of the interior angles is equal to 180°. We know one angle is 35°, and the other is 90°. Added together, that is 125°. Now just subtract 125° from 180°, and you get 55°.
m∠ABC = 95°
Here's why: Once again, the sum of the interior angles is equal to 180°. We know m∠A is 35°, and that the m∠C is 60°. Added together, that is 95°. Subtract that from 180°, and you get 85°.
Hope that helps!
P.S. whenever you are asked find the m∠ABC, or any three letters, you have to find the measure of the angle of the middle letter. So when asked, find m∠DEF, they want the angle of E. Another example is when asked find m∠ABC, you have to find the measure of angle B. Hope that makes sense, and that will help oin the future!