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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

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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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