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# The Given Figure Shows a Circle with Centre O Such that Chord Rs is Parallel to Chord Qt, Angle Prt = 20° and Angle Poq = 100°. Calculate: (Iv) Angle Str - ICSE Class 10 - Mathematics

ConceptArc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse

#### Question

The given figure shows a circle with centre O such that chord RS is parallel to chord QT, angle PRT = 20° and angle POQ = 100°. Calculate:

(iv) angle STR

#### Solution

Join PQ, RQ and ST.

Since RSTQ is a cyclic quadrilateral
∴ ∠QRS + ∠QTS = 180° (sum of opposite angles)
⇒  ∠QRS + ∠QTS + ∠STR = 180°
⇒ 110 + 40  + ∠STR =  180°
⇒ ∠STR =  30°

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Solution The Given Figure Shows a Circle with Centre O Such that Chord Rs is Parallel to Chord Qt, Angle Prt = 20° and Angle Poq = 100°. Calculate: (Iv) Angle Str Concept: Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse.
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