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Triangle and Sum of Its Internal Angles

In Δ PQR,if ∠...

Question

$I n Δ P Q R, i f ∠ P - ∠ Q = 42^{\circ} a n d ∠ Q - ∠ R = 21^{\circ}, f i n d ∠ P, ∠ Q a n d ∠ R .$

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Solution

Given: ∠P - ∠Q = 42° and ∠Q - ∠R = 21°
Then,
∠P = 42° + ∠Q and ∠R = ∠Q - 21°

∴ 42° + ∠Q + ∠Q + ∠Q - 21° = 180° [Sum of the angles of a triangle]

⇒ 3∠Q = 159°

⇒ ∠Q = 53°

∴ ∠P = 42° + ∠Q =42° + 53° = 95°

∴ ∠R = ∠Q - 21° = 53° - 21° = 32°

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∠ P - ∠ Q = 42^{\circ}

∠ Q - ∠ R = 21^{\circ}

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In 🔺 PQR, if angle P - angle Q = 42° and angle Q - angle R =21°.Find angle P, angle Q and angle R

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