Question

In the triangle ABC measures of angles angle a is 46 and Angle c is 60 are given . the angle bisector intersects the circumcised circle about the triangle ABC in points C and D the measure of the angle CBD?​

Answer 1

Answer:

Step-by-step explanation:

104 digree

Answer 2

The measure of the angle CBD is 104 degree

Given,

In ΔABC,

∠A = 46 degree

∠C = 60 degree

Angle bisector intersects a circumcircle at points C and D

To Find,

∠CBD = ?

Solution,

We have been given that ∠A = 46 degree and ∠C = 60 degree

We know that the sum of all interior angles of a triangle equals 180 degree

⇒ ∠A + ∠B + ∠C = 180

⇒ 46 + ∠B + 60 = 180

⇒ 106 + ∠B = 180

⇒ ∠B = 180 - 106 = 74 degree

⇒ ∠CBA = 74 degree

Now we have been given that the angle bisector intersects a circumcised circle at points C and D.

That is, the angle bisector bisects ∠BCA and this bisector intersect the circle at a point D outside the triangle

Therefore, ∠BCD = ∠BCA / 2 = 60/2 = 30 degree

Also, ∠BAC = ∠BDA = 46 degree (since they are angles in the same segment of the circle)

Further, ΔCBD had angles ∠B = x degree, ∠C = 30 degree, and ∠D = 46 degree

Our required angle is x

Sum of angles of a triangle = 180

⇒ ∠C + ∠B + ∠D = 180

⇒ 30 + x + 46 = 180

⇒ x +76 = 180

⇒ x = 104 degree

#SPJ2