Answer:
a = 33°
b = 115°
c = 75°
d = 58°
f = 65°
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°