Find the measures of the numbered angles in isosceles trapezoid for question

Because it's iscosceles, angle 1 is similar size to the angle on the right leg.
∠1 = 67°

The sum of interior angles in trapezoid equals to 360°.
And because it's iscosceles, the upper angles are in the same size. We can write it as,
the sum of angles = 360°
67° + 67° + ∠2 + ∠2 = 360°
134° + 2 × ∠2 = 360°
2 × ∠2 = 360° - 134°
2 × ∠2 = 226°
∠2 = 113°

Final answer
∠1 = 67°
∠2 = 113°

x = 27

Step-by-step explanation:

The little square at the bottom of the figure means that that angle is a right angle, or 90°. Knowing that it's a 90° angle and that one section of the adjacent angle is 63°, we just calculate 90-63 to get 27, the value of x.