Question

In the given figure, PQ is a tangent to a circle with centre O, at a point B. If angle AOB = 100° then find angle ABP ​

Answer 1

50 is the correct answer

Answer 2

Answer:

➡️ given=LAOB=100⁰,PQ is a tangent to a circle

➡️to find=ABP=?

➡️ solution

✳️ construct the triangle formed AOB,we find that the sides are equal

OA=OB(radius of the circle)

✳️it indicates that the rest two are equal

✳️Let the angle be x(since both are same)

✳️by angle sum property of a triangle we get

➡️100⁰+x+x=180⁰

➡️2x=180⁰-100⁰

➡️2x=80⁰

➡️x=80⁰

____

2

➡️x=40⁰

✳️Now we know that PB is perpendicular to OB,as PQ is tangent to circle and tangent is always perpendicular

✳️So LOBP=90⁰

➡️LOBA+LABP=90⁰

➡️40⁰+LABP=90⁰

➡️LABP=90⁰-40⁰

➡️LABP=50⁰

✳️ therefore LABP us 50⁰

Step-by-step explanation:

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