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

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°