**CHALLENGE** Find all of the missing angles - a, b, c, and d.

a = 65°

d = 75°

b  = 25°

c = 25°

Explanation:

To solve the given problem, we are going to use different angle theorems.

Using these theorems, it would be possible to establish the relationship between the unknown and given angles.

A.

To solve for angle a, we are going to use the concept of angles on a straight line.

    The sum of angles on a straight line is 180°

 Therefore;

             60 + 55 + a  = 180

                   115 + a  = 180

                            a = 180 - 115

                            a = 65°

B. To solve for angle d, we are going to use the concept of right angles.

   Angle in a right angle is 90°;

            So:

                  d + 15 = 90

                   d = 90-15 = 75°

C. To find angle, b, since we know a, we use angles in a right angle triangle.

   Sum of angles in triangle  = 180°

       a + b + 90 = 180

            b = 180 - 90 -a

            b = 90 - 65 = 25°

D. Angles b and c are vertically opposite and can be said to be the same.

  So b = c

             c  =  25°