I need to find the missing angle measures.

a. 78

b. 102

c. 78

Step-by-step explanation:

step 1. b = 102° (vertical angles)

step 2. one complete revolution equals 360°

step 3. a + b + c + 102 = 360

step 4. a + 102 + c + 102 = 360

step 5. a + c = 156°

step 6. 2a = 156 (vertical angles are equal)

step 7. a = 78°, c = 78°.

step-by-step explanation:

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm