Each angle was found using the principles of circles.
How do relate the angle at the circumference and angle at the centre made by the same arc?
The angle of the circumference is half of the angle at the centre of the circle by an arc.
AB = 78°
∠5 = 39°
Angles intercepted by the same arc are equal.
∠4 = 39°
FE= 105°
∠16 =105°
ED = 27°
∠17 =27°
CD = 42°
∠10 =21°
∠3 =21°
The angle of the semi-circle is 90°.
∠2 =90°
∠8=∠9 = (180-48)/2
∠8= 66°
∠9= 66°
∠7=90°-∠8 = 90°-66°
∠7=24°
∠17 = 180°-∠15-∠16
∠17 = 180°-48°-105°
∠17 =27°
∠6=∠15/2 = 48/2
∠6=24°
∠21 = 180°-∠7-∠16
∠21 = 180°-24°-105°
∠21 =51°
∠19 =51°
∠18 = 180°-∠17-∠6
∠18 = 180°-27°-24°
∠18 = 129°
∠20 = 129°
BC = 60°
∠1 = 60/2
∠1 =30°
∠11=180°-∠1-∠2
∠11=180°-30°-90°
∠11=60°
∠13=60°
∠12=180-∠11
∠12=180°-60°
∠12=120°
∠14=120°
∠15=48°
Hence, Each angle was found using the principles of circles.
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