$Δ P Q R = Δ A B C$ if $P Q = 5 c m . ∠ Q = 40^{0}$ and $∠ P = 80^{0}$ then which of the following are true?

A B = 5 c m, ∠ A = 60^{0}

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A B = 5 c m, ∠ C = 60^{0}

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B C = 5 c m, ∠ C = 60^{0}

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B C = 5 c m, ∠ B = 40^{0}

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Solution

The correct option is B $A B = 5 c m, ∠ C = 60^{0}$
In $△ P Q R$ using angle sum property of triangle
$∠ P + ∠ Q + ∠ R = 180^{\circ} 80^{\circ} + 40^{\circ} + ∠ R = 180^{\circ} \Rightarrow ∠ R = 180^{\circ} - 120^{\circ} = 60^{\circ}$

Now $△ P Q R ≅ △ A B C$
As corresponding parts of congruent triangle are equal
$∴ A B = P Q = 5 c m$ and $∠ C = 60^{\circ}$

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ΔPQR=ΔABC if PQ=5cm.∠Q=400 and ∠P=800 then which of the following are true?

The correct option is B AB=5cm,∠C=600In △PQR using angle sum property of triangle∠P+∠Q+∠R=180∘80∘+40∘+∠R=180∘⇒∠R=180∘−120∘=60∘Now △PQR≅△ABCAs corresponding parts of congruent triangle are equal∴AB=PQ=5cm and ∠C=60∘

$Δ P Q R = Δ A B C$ if $P Q = 5 c m . ∠ Q = 40^{0}$ and $∠ P = 80^{0}$ then which of the following are true?