Question
Download Solution PDFP, Q, R and S are four points on a circle. PR and QS intersect at a point X such that ∠QXR = 120° and ∠XRS = 10°. The measure of ∠QPR is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
P, Q, R, S are points on a circle.
PR and QS intersect at X.
∠QXR = 120°
∠XRS = 10°
Concept Used:
The sum of angles in a triangle is 180°.
Angles subtended by the same arc at the circumference are equal.
Calculation:
∠XSR + ∠SRX = 120° [Exaternal angle theorm]
⇒ ∠XSR + 10° = 120°
⇒ ∠XSR = 110°
∠QPR and ∠QSR subtend the same arc QR, therefore ∠QPR = ∠QSR
⇒ ∠QPR = 110°
The measure of ∠QPR is 110°.
Last updated on Dec 9, 2024
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