Question

PQ is tangent to the circle with centre at O, at the point B. IF
AOB = 100°, then < ABP is equal to
(AS
(B)
(C)
(D)
50°
40°
60°
80°​

Answer 1

the correct answer is

(A) 50°

Answer 2

PQ is tangent to the circle with centre at O, at the point B. The given angle AOB= 100 Degree . Angle ABP is equals to 50 degree. The step wise explanation is given below:

- PQ is tangent to the circle with centre at O,at point B

So, ∠OBP=90°

and it is given that ∠AOB=100°

Find=∠ABP

- Now, in ΔAOB

AO =BO.

So,∠OBA=∠OAB. ...(1)

(sum of all angles of triangle is 180°)

∠OBA+∠OAB+∠AOB=180°

∠OBA+∠OBA+100°=180° [BY..(1)]

2∠OBA=180°-100°

2∠OBA=80°

∠OBA=80°/2

∠OBA=40°

- Now, ∠OBP=90°

∠OBP=∠OBA+∠ABP

90°=40°+∠ABP

∠ABP=90°-40°

∠ABP=50°

- SO, the right option is (A) 50°