Answer:
∠3 = 18°
∠4 = 144°
∠2 = 36°
∠1 = 72°
Step-by-step explanation:
From the concept of alternate interior angles,
∠3 = 18°
Since the diagonal divides the rectangle into 4 parts with 2 of the rectangles being similar.
Then, the triangle with ∠3 & ∠4 is an Isosceles triangle and as such;
∠4 = 180 - 2(∠3)
∠4 = 180 - 2(18)
∠4 = 180 - 36
∠4 = 144°
∠2 = 180 - ∠4 (because sum of angles on a straight line is 180°)
∠2 = 180 - 144
∠2 = 36°
Like it was done for angle ∠4 above;
∠1 = (180 - 36)/2
∠1 = 144/2
∠1 = 72°
