Question

(i) If ZAOB = 126°, what is ZAPB? (ii) If ZOAB = 29°, what is ZAPB? (iii) If ZAPB = 62°, what is ZOBA? ​

Answer 1

Answer:

i) angle APB = angle AOB/2

= 126/2

= 63°

ii) angle OAB = angle OBA = 29° (since OA = OB = radii of the circle)

=> By sum angle property (in triangle OAB):

angle AOB = 180 - 58

= 122°

=> angle APB = 122/2

= 61°

iii) angle AOB = 2 × angle APB

= 2 × 62

= 124°

In triangle OAB:

angle OAB = angle OBA = x (since OA = OB)

=> By sum angle property (in triangle OAB):

2x = 180-124

=> x = 56/2

= 28°

Hope this helped.

Answer 2

I)angle APB=63 degree
Angle at centre is equal to twice the angle at circumference
II)angle OAB is 29 degree then angle AOB will be 122 degree so
Angle APB=61 degree using the same property
iii) angle APB is 62 degree so angle AOB will be 124 using the same property
AngleOBA+angle OAB+angleAOB=180
Angle OAB=angleOBA
So 2*angleOBA+124=180
2*angleOBA=180-124=56
Angle OBA=56/2=28 degree