It seems like you're working on a problem involving an isosceles trapezoid, and you need to find the measure of the numbered angles.

From the image, we can see that the trapezoid has one of the angles labeled as 52°, and the other angle is at the opposite vertex. Since this is an isosceles trapezoid, the base angles are congruent, meaning the angles on the same side of the trapezoid must be equal.

• The angle marked as 1 will be supplementary to the 52° angle. Supplementary angles add up to 180°.

Therefore, we can calculate angle 1 as: $m\angle 1 = 180^\circ - 52^\circ = 128^\circ$

Let me know if you'd like further details or have other questions!

Here are 5 questions to expand on this topic:

1. What is the property of the base angles in an isosceles trapezoid?
2. How do you calculate the sum of interior angles in any polygon?
3. How would the angles change if the trapezoid were not isosceles?
4. How do you calculate the area of an isosceles trapezoid?
5. Can you apply this knowledge to solve for missing angles in other quadrilaterals?

Tip: Remember that the sum of the interior angles of any quadrilateral is always 360°.