Question

I've been trying for hours but i cant seem to solve this I need help i understand if you don't want too since its my work but all videos i find online are so difficult to grab and understand.
Ive attached the image!

Answer 1

FIRST
I solve the angles on the center (2,3,4)
∠2 is as big as 121° because they are vertical angles
∠3 is as big as ∠4 because they are vertical angles
The sum of angles on the center is 360° because they make a round of circle
121° + ∠2 + ∠3 + ∠4 = 360°
121° + 121° + ∠3 + ∠3 = 360°
242° + 2(∠3) = 360°
2(∠3) = 118°
∠3 = 59°
∠4 = 59°

SECOND
I want to find angle on the left (1) with interior angles of triangle
The sum of interior angles in triangle = 180°
∠1 + ∠3 + 48° = 180°
∠1 + 59° + 48° = 180°
∠1 = 73°

THIRD
I'm going to the right triangle. The right triangle is congruent with the left triangle. So the angles that facing each other has the same number.
∠7 = 48°
∠6 = ∠1 = 73°

FOURTH
I'm going to the upper triangle and find ∠5
The sum of interior angles in triangle = 180°
35° + ∠2 + ∠5 = 180°
35° + 121° + ∠5 = 180°
∠5 = 24°

LAST
I'm going to the lower triangle. The lower triangle is congruent with the upper triangle. So the angles that facing each other has the same number.
∠8 = 35°
∠9 = ∠5 = 24°

THE SUMMARY
∠1 = 73°
∠2 = 121°
∠3 = 59°
∠4 = 59°
∠5 = 24°
∠6 = 73°
∠7 = 48°
∠8 = 35°
∠9 = 24°