Question

in the given figure ,if o is the centre of circle determine angle APB​

Answer 1

Answer:

The sum of adjacent sides of a triangle is 90°

Angle APB=90°

Step-by-step explanation:

In ∆ AOB

Angle B = 30°

so angle A= 60°

By angle sum property

30+60+O=180°

O= 180-90

O= 90

The opposite side of 90° angle is known as hypotenuse so AB is hypotenuse or longest side.

And AB is common in both Triangles so in ∆ ABP,

hypotenuse is AB.

so Value of angle P = 90°

Because if there is a hypotenuse, the triangle is right angle triangle.

Answer 2

Answer:

120°

Step-by-step explanation:

let there be a point Q on the circumference on opposite side of P

<OAB = 30° as ∆OAB is isosceles

So, <AOB = 180-30-30 = 120°

So, <AQB = ½ * 120° = 60°

(as angle subtended by a chord on circumference is half of the angle subtended by it at the centre of the circle)

As, PAQB is a cyclic quadrilateral

So sum of opposite angles is 180°

So, <P = 180° - <Q = 180-60 = 120°

i hope this helps u