#### 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:

(iii) angle QRS

#### Solution

Join PQ, RQ and ST.

RS ∥ QT

∴ `∠`SRT = `∠`QTR (alternate angles)

But `∠`QTR = 40°

∴ `∠`SRT = 40°

Now,

`∠`QRS = `∠`QRP + `∠`PRT + `∠`SRT

⇒ `∠`QRS = 50° + 20° + 40° = 110°

Is there an error in this question or solution?

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: (Iii) Angle Qrs Concept: Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse.