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प्रश्न
If ΔABC ∼ ΔDEF such that ∠A = 92° and ∠B = 40°, then ∠F = ?
पर्याय
52°
92°
40°
48°
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उत्तर
48°
Explanation:
Given: ∠A = 92°, ∠B = 40°.
Since, ΔABC ∼ ΔDEF
So, ∠A ≅ ∠D, ∠B ≅ ∠E and ∠C ≅ ∠F
⇒ ∠D = 92°, ∠E = 40°
In ΔDEF,
∠D + ∠E + ∠F = 180°
⇒ 92° + 40° + ∠F = 180°
⇒ ∠F = 180° – 132° = 48°
Thus, ∠F = 48°
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solution:
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Ray MX is the bisector of ∠PMQ.
∴ `("MP")/("MQ") = square/square` .............(I) [Theorem of angle bisector]
Similarly, in ∆PMR, Ray MY is the bisector of ∠PMR.
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But `("MP")/("MQ") = ("MP")/("MR")` .............(III) [As M is the midpoint of QR.]
Hence MQ = MR
∴ `("PX")/square = square/("YR")` .............[From (I), (II) and (III)]
∴ XY || QR .............[Converse of basic proportionality theorem]
