Question

In the given figure . BOC is a Diameter of the circle and AB=AC. Then

Answer 1

Answer:

45° is the answer.

Step-by-step explanation:

Given: BOC is a diameter of the circle.

AC=AB

Here, BAC forms a semicircle.

We know that angle in a semicircle is always 90°.

A.T.Q.

∠BAC = 90°

Here ∠ABC = ∠ACB

We know that sum of all the angles in the triangle is 180°.

That is,

∠ABC + ∠ACB + ∠BAC = 180°

=> 2 × ∠ABC + ∠BAC =180°

=> 2 × ∠ABC + 90° =180°

=> 2 × ∠ABC = 180°-90°

=> 2 × ∠ABC = 90°

=> ∠ABC = 90°/2

=> ∠ABC = 45°

Hope it helps you!!

Answer 2

Answer:

               ∠ABC = 45°

Step-by-step explanation:

Answer:

Given = BOC is a diameter of a circle.

             AB=AC

To Find = ∠ABC =?

Solution = Here, ∠BAC forms a semicircle.

                ∠BAC=90°                         .........(i)

                Here ∠ABC = ∠ABC

   ∴ By the property of triangle the sum of all angles in the triangle is 180°

             ∠ABC + ∠ACB + ∠BAC =180°

             =2 ×∠ABC + BAC =180°

             =2 ×∠ABC + 90°= 180°

            =2 ×∠ABC =180° - 90°

            =2 ×∠ABC =90°

              ∠ABC = 90°                                

                             2  

          =∠ABC = 45°