Question

In fig ab is a chord of a circle pq is a tangent at a point b of circle if angle aob is 110 degree then angle abq is.....​

Answer 1

∠ ABQ = 125°

Step-by-step explanation:

See the attached diagram.

In Δ ABO, OA = OB = Radius of the circle

So, Δ ABO is an isosceles triangle and ∠ OAB = ∠ OBA and ∠ AOB = 110° {Given}

So, ∠ OBA + ∠ OAB + ∠ AOB = 180°

⇒ 2∠ OBA + 110° = 180°

⇒ 2 ∠ OBA = 70°

⇒ ∠ OBA = 35°

Now, ∠ ABQ = ∠ OBA + ∠ OBQ = 35° + 90° = 125° (Answer)

{Since PQ is a tangent to circle with center O at point B, hence ∠ OBQ = ∠ OBP = 90°}

Answer 2

Answer:

OA and OB are the radii of the circle. According to the theorem radius is perpendicular to tangent. Therefore, angle OBQ=90 degree

OAB is an isosceles triangle, so angles OAB and OBA will both be 35 degree

As,

    OBQ = OBA + ABQ

    90 = 35 + ABQ

    ABQ = 90 - 35

    ABQ = 55

Step-by-step explanation:

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