Answer:
A.
1. 70
2. 60
3. 65
4. 35
5. 25
6. 60
7. 130
8. 50
9. 180
10. 50
B.
1. 22.5°
2. 27°
3. 90°
Step-by-step explanation:
A.
Given:
mAB = 70
mCD = 50
1. m∠APB = mAB (angle APB is equal to arc AB)
m∠APB = 70
2. m∠BPC = mBC (the measure of angle BPC is equal to arc BC)
mAB + mCD + mBC = 180 (the three minor arcs form a semi-circle, which has a degree measure of 180)
70 + 50 + mBC = 180 (substitute with the given values)
120 + mBC = 180
120 - 120 + mBC = 180 - 120 (subtract 120 from both sides)
mBC = 60
m∠BPC = 60
3. m∠ADC = mABC/2 (angle ADC is an inscribed angle. the measure of an inscribed angle is half the measure of its intercepted arc)
m∠ADC = (mAB + mBC)/2 (the measure of arc ABC is equal to the sum of arc AB and arc BC)
m∠ADC = 70 + 60/2 (substitute values)
m∠ADC = 130/2
m∠ADC = 65
4. m∠ADB = mAB/2 (angle ADB is an inscribed angle. its measure is half the measure of its intercepted arc which us arc AB)
m∠ADB = 70/2
m∠ADB = 35
5. m∠DAC = mCD/2
m∠DAC = 50/2
m∠DAC = 25
6. mBC = 60 (we already solved for this in number 2)
7. mABC = mAB + mBC (arc ABC is equal to the sum of arc AB and arc BC)
mABC = 70 + 60
mABC = 130
8. mCD = 50 (this value was already given)
9. mACD = 180 (arc ACD is a semi-circle so its measure is 180 or for solution's sake, you can just add the measurements of arc AB, arc BC, and arc CD)
10. m∠CPD = mCD (angle CPD is equal to arc CD)
m∠CPD = 50
B.
1. x = 45/2
x = 22.5
2. x = 27 (the intercepted arc of the given 27 is 54, they have the same intercepted arc with x which makes it 27)
3. x = 180/2 (this inscribed angle has an intercepted arc of 180. as you can see, it forms a triangle with the diameter, which is 180°. since its intercepted arc is 180°, then this inscribed angle's measurement should be half the arc)
x = 90
