Question

the given figure, find the measure angle a b c​

Answer 1

Answer:

the question they have mentioned ABCD is a cyclic quadrilateral, the quadrilateral which is inscribed in the circle and whose vertices lie on the same circle. By figure we know the value of some angles by using this we have to determine the value of the angle B.

Now consider the △BYC△BYC , we know the value of ∠Y∠Y and ∠C∠C we can determine the value of ∠B∠B . As we know that the sum of all angles in the triangle is 180∘180∘ . Therefore, we have ∠B+∠Y+∠C=180∘∠B+∠Y+∠C=180∘ .------- (1)

  ∠Y=62∘∠Y=62∘ and ∠C=82∘∠C=82∘ are the known value. Substitute these values in the equation (1)

  ∠B+62+82=180∘∠B+62+82=180∘

On applying the addition

 ⇒∠B+144=180⇒∠B+144=180

Move 144 to the RHS

 ⇒∠B=180−144⇒∠B=180−144

On further simplification

 ⇒∠B=36