Question

find the measures of all the angles in the rectangle.
(rectangle image with angles labeled 1,2,3,4,5 and a 24° angle)
m∠1 = (label optional)

Explanation:

Step1: Identify right angles in rectangle

All rectangle angles are 90°. So ∠1=∠4=90°.

Step2: Find ∠5

In the triangle, ∠5 + 24° = 90° → ∠5=66°.

Step3: Find ∠3

∠3=∠5=66° (alternate interior angles, since rectangle sides are parallel).

Step4: Find ∠2

In the triangle, ∠2 + 24° + ∠3=180° → ∠2=180-24-66=90°.

Answer:

∠1=90°, ∠2=90°, ∠3=66°, ∠4=90°, ∠5=66°