Question

. In the figure, XAY is a tangent to the circle
with centre o at A. If
Angle BAX = 70°, Angle BAQ = 40°, then Angle ABQ is
equal to​

Answer 1

Given:

∠BAQ =40°

∠BAX=70°

XAY is the tangent.

To Find:

∠ABQ

Solution:

∠QAX=∠BAX-∠BAQ

          =70°-40°

          =30°

By Alternate Segment Theorem,

∠ABQ=∠QAX

          =30°

Hence the value of ∠ABQ is 30°

Answer 2

The value of angle ∠ABQ in the ΔABQ will be 30°.

Step-by-step process

Given:

The value of ∠BAX = 70°

The value of ∠BAQ = 40°

To find: ∠ABQ

Solution:

Let us extend the line BQ to intersect the tangent AX.

We know that the tangent forms a right angle with the diameter of the circle.

So, ∠EAX = 90°

Now, ∠QAX = ∠BAX-∠BAQ

∠QAX  = 70-40= 30°

From the alternate segment theory of angles of a triangle, we can say that:

∠ABQ = ∠QAX

So,∠ABQ = ∠QAX = 30°

Result:

Therefore, the value of angle ∠ABQ is 30°.

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