Use the diagram to find each angle measure.

a = 33°

b = 115°

c = 75°

d = 58°

f = 65°

Step-by-step explanation:

The 90 degree angle to the left (L shaped) PLUS angle d PLUS 32 degree angle forms a straight line. A straight line is 180 degrees. Thus we can write an equation and solve for d:

90 + d + 32 = 180

122 + d = 180

d = 180 - 122

d = 58°

Now, Looking at left triangle (c, d, 47 angles), we see that it comprises of angle c, angle d, and 47 degree angle. We know that sum of 3 angles in a triangle is always 180. So we can write an equation and solve for c:

c + d + 47 = 180

c + 58 + 47 = 180

c + 105 = 180

c = 180 - 105

c = 75°

Then,

The angle 47 and angle a falls in a straight line. Again, straight line is equal to 180 degrees. So we can write an equation and solve for a:

47 + a = 180

a = 180 - 47

a = 33°

Now, the large triangle comprises of 32 degree angle, angle a and angle b. We know sum of 3 angles in a triangle is always 180. So we can write an equation and solve for b:

32 + a + b = 180

32 + 33 + b = 180

65 + b = 180

b = 180 - 65

b = 115°

Lastly,

Angle b and Angle f makes a straight angle (straight line). A straight angle is 180 degrees. Now, we can write an equation and solve for f:

b + f = 180

115 + f = 180

f = 180 - 115

f = 65°

6e14 is the answer.