Find the measures of the numbered angles in the kite? (image below please help)

answer

1, 2, 3, 4 = 90 degrees

5 = 41 degrees

6 = 39 degrees

7, 9 = 51 degrees

8, 10 = 49 degrees

step-by-step explanation

since this is a kite, the lengths p and q (the diagonals of the kite) are perpendicular to each other, so angles 1, 2, 3, and 4 are all 90 degrees

to find angle 5, we know that the kite is symmetric across the horizontal diagonal, so angle 5 would be the same as 41 degrees

to find angle 6, we also look at symmetry, so angle 6 is the same of 39 degrees

to find angle 7, all three angles in a triangle, bottom left, must add up to 180. since we know angle 3 = 90 and angle 6 = 39, angle 7 = 180 - 90 - 39 = 51 degrees

because of symmetry, angle 9 would be equal to angle 7 = 51 degrees

to find angle 8, all three angles in a triangle, bottom right, must add up to 180. since we know angle 4 = 90 and angle 5 = 41, angle 8 = 180 - 90 - 41 = 49

because of symmetry, angle 10 would be equal to angle 8 = 49

  or  

sin y = 7/q

7 is the opposite side length, q is the hypotenuse

tan y = 7/r

7 is the opposite side length, r is the adjacent side length

using sohcahtoa ^^^^

cos y = adjacent/hypotenuse

cos y = r/q