Given circle P with arc AE=53, arc BA=68 and arc CB=72 match the following angles with their corresponding measurements

From the diagram;

1. Angle 2 = ADB+BDH

= arcAB/2 + 90

= 34 + 90

= 124°

2. Angle 4 = 90°,

Reason; the angle between a tangent and a radius is equal to 90. A tangent is a line that touches the circumference of a circle once even if prolonged.

3. Angle 5 = 90 - BDC (note the acr subtends twice the angle it subtends on the circumference to the center.

= 90-arc BC/2

= 90-36

= 54°

4. Angle 6 = BFD

= 180-ADB-FBD

= 180-AB/2-DE/2

But DE = 180 - 121 = 59

Therefore, BFD = 180 - 34-29.5

= 116.5°

5. Angle 1 = 180 - BFD (angles on a straight line add up to 180°)

= 180 - 116.5

= 63.5°

6. Angle 3 = 180 - (ADB+BFD)

= 180 - (34 + 116.5)

= 180 - 150.5

= 29.5°

similarly angle 3 = DE/2 = 59/2 = 29.5°

7. Angle 8 = 90, because BD is diameter;

angles subtended by a diameter to the circumference is always a right angle (90°)

8. Angle 7 = BE

but BE = AB+AE

= 68 + 53

= 121°