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Question
In the figure, chord LM ≅ chord LN, ∠L = 35°.
Find
(i) m(arc MN)
(ii) m(arc LN)
Solution
(i) ∠L = `1/2` m(arc MN) ...[Inscribed angle theorem]
∴ 35° = `1/2` m(arc MN)
∴ 2 × 35° = m(arc MN)
∴ m(arc MN) = 70°.
(ii) In ∆LMN,
chord LM ≅ chord LN
∴ ∠M = ∠N ...[Isosceles triangle theorem]
∴ ∠L + ∠M + ∠N = 180° ...[Sum of the measures of angles of a triangle is 180°]
∴ 35° + ∠M + ∠M = 180°
∴ 2∠M = 180° – 35° = 145°
∴ ∠M = `145^circ/2`
Now, m(arc LN) = 2 × ∠M ......[Inscribed angle theorem]
= `2 xx 145^circ/2`
= 145°
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