Question

PQ and PR are tangents to the circle with centre O and S is a point on the circle such that angle SQL=50° and angle SRM=60°.Find angle QSR..... figure is in photo

Answer 1

Answer:

Step-by-step explanation:

Join Q to R

<QSR = <SQL = 50 degrees

<RQS = <MRS = 60 degrees

Angle between a chord and a tangent equals the angle subtended by the chord at the circumference in the segment opposite the angle

∴ <QSR = 180 - (60+50) = 70 Degrees (Angles of a triangle add up to 180 degrees)

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Answer 2

Answer:

∠QSR = 50°

Step-by-step explanation:

Given : ∠SQL = 50 and ∠SRM = 60

First join the points Q and R to form a triangle QSR

Now, by using the theorem that the angle subtended by the chord and the tangent is equal to the angle formed by the chord at the circumference in the opposite segment.

⇒ ∠SQL = ∠SRQ = 50

and ∠SRM = ∠RQS = 60

Now, in ΔQSR by using angle sum property

∠QSR + ∠RQS + ∠SRQ = 180

⇒ ∠QSR = 180 - 130

⇒ ∠QSR = 50°