If in PQR and LMN- - P - - M - 60- PQ - ML - PR - MN and - N - 55- then - Q is-

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Properties of Isosceles and Equilateral Triangles

If in PQR a...

Question

If in $△ P Q R$ and $△ L M N$ , $∠ P = ∠ M = 60^{\circ}$ , $P Q : M L = P R : M N$ and $∠ N = 55^{\circ}$ , then $∠ Q$ is:

50^{\circ}

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55^{\circ}

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65^{\circ}

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75^{\circ}

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Solution

The correct option is C $65^{\circ}$
As per S-A-S criteria It is clear that $Δ$ PQR and LMN are similar
$∴ ∠ R = ∠ N = 55^{\circ}$
Hence, $∠ Q = 180^{\circ} - (∠ P + ∠ R)$
$= 180^{\circ} - (60^{\circ} + 55^{\circ}) = 65^{\circ}$

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If in △PQR and △LMN, ∠P=∠M=60∘, PQ:ML=PR:MN and ∠N=55∘, then ∠Q is:

The correct option is C 65∘As per S-A-S criteria It is clear that Δ PQR and LMN are similar∴∠R=∠N=55∘Hence, ∠Q=180∘−(∠P+∠R)=180∘−(60∘+55∘)=65∘

If in $△ P Q R$ and $△ L M N$ , $∠ P = ∠ M = 60^{\circ}$ , $P Q : M L = P R : M N$ and $∠ N = 55^{\circ}$ , then $∠ Q$ is:

The correct option is C $65^{\circ}$
As per S-A-S criteria It is clear that $Δ$ PQR and LMN are similar
$∴ ∠ R = ∠ N = 55^{\circ}$
Hence, $∠ Q = 180^{\circ} - (∠ P + ∠ R)$
$= 180^{\circ} - (60^{\circ} + 55^{\circ}) = 65^{\circ}$