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Answers
→Given: m(arc QDS) = 130°, m(arc PCR) = 40°
→To find: m(AQP), m(SRQ), m(SAQ)
→Solution: We know, if two lines containing chords of a circle intersect each other outside the circle, then the measure of the angle between them is half the difference in measures of the arcs intercepted by the angle.
⇒ ∠AQP = ½ × m(arc QDS) - m(arc PCR)
⇒ ½ ×( 130 - 40)
⇒ ½ ×(90)
⇒ 45° is ∠AQP
We also know that the measure of an angle is equal to its arc opposite arc.
⇒ ∠ SRQ = m(arc PCR)
⇒ ∠SRQ = 40°
⇒ ∠SAQ = m(arc QDS)
⇒ ∠SAQ = 130°
- ∴ ∠AQP = 45°
- ∴ ∠SRQ = 45°
- ∴ ∠SAQ = 130°
⇒ Learn more: https://brainly.in/question/14763568
∠AQP = ½ × m(arc QDS) - m(arc PCR)
⇒ ½ ×( 130 - 40)
⇒ ½ ×(90)
⇒ 45° is ∠AQP
We also know that the measure of an angle is equal to its arc opposite arc.
⇒ ∠ SRQ = m(arc PCR)
⇒ ∠SRQ = 40°
⇒ ∠SAQ = m(arc QDS)
⇒ ∠SAQ = 130°
∴ ∠AQP = 45°
∴ ∠SRQ = 45°
∴ ∠SAQ = 130°