Question

in figure pq and pr are two tangents to a circle with centre o. if angle QPR=80° then find angle QOR​

Answer 1

Answer:

angle QOR =100°

Step-by-step explanation:

angle QOR+QPR=180°

angle QOR+80°=180

angle QOR =180°-80°

angle QOR=80°

Answer 2

Answer:

the required angle of ∠QOR  is 100°

Step-by-step explanation:

Explanation:

Given , PQ and PR are two tangents to a circle with centre O

and ∠QPR = 80°

OQ=OR     (radius of circle )

As  we know , the radius from the centre of the circle to the point of tangency is perpendicular to the tangent line .

So , OQ is perpendicular to the tangent PQ at Q.

    ⇒ ∠OQP = 90 °

Similarly , OR is perpendicular to the tangent PR at R .

⇒ ∠ORP = 90 °

Step 1:

OQPR is a quadrilateral .

Therefore , ∠OQP+∠QPR+∠PRO+∠ROQ = 360

Sum of angle of a quadrilateral is 360°

                90 + 80 +90 +∠ROQ = 360

         ⇒260 +∠ROQ = 360

          ⇒∠ROQ = 360 - 260 = 100°

∠ROQ = ∠QOR = 100

Final answer :

Hence , the angle ∠QOR is 100°.