Q. 715.0( 3 Votes )

One of the angles of a triangle is 65°. Find the remaining two angles, if their difference is 25°.

Answer :

In Δ ABC, let ∠ A = 65° ………….(i)
       ∠ B - ∠ C = 25° ……………………….(ii)
∠ A + ∠ B + ∠ C = 180° [ Sum of the angles of a Δ is 180° ]
⇒ 65° + ∠ B + ∠ C = 180°
     ⇒ ∠ B + ∠ C = 180° - 65°
     ⇒ ∠ B + ∠ C = 115° …………………….(iii)
Adding (ii) and (iii),
2∠ B = 140°
⇒ ∠ B = = 70°
Substituting in (iii), 70° + ∠ C = 115°
⇒ ∠ C = 115 - 70° = 45°
∴ ∠ B = 70° and ∠ C = 45°.

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