Question

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

Answer 1

Angle 1 = 63.5

Angle 2 = 124

Angle 3 = 29.5

Angle 4 = 90

Angle 5 = 54

Angle 6 = 116.5

Angle 7 = 121

(all are degrees)

Answer 2

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°