#### 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:

(i) angle QTR

#### Solution

Join PQ, RQ and ST.

i)

`∠`POQ + `∠`QOR = 180°

⇒ 100° + `∠`QOR = 180°

⇒ `∠`QOR = 80°

Arc RQ subtends `∠`QOR at the centre and `∠`QTR at the remaining part of the circle.

∴ `∠QTR =1/2 ∠QOR`

⇒ `∠QTR = 1/2 xx 80° = 40°`

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