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°.

∠ 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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PREVIOUSFill in blanks in each of the following to make the statement true: (i) If two parallel lines are intersected by a transversal, then each pair of corresponding angles are …………..(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ……………(iii) Two lines perpendicular to the same line are ………….. to each other.(iv) If a transversal intersects a pair of lines in such a way that a pair of alternate angles are equal, then the lines are ………….(v) Two lines parallel to the same line are ……………to each other.(vi) If a transversal intersects a pair of lines in such a way that the sum of interior angles on the same side of the transversal is 180°, then the lines are …………. NEXTIf the angles of a triangle are in the ratio 2 : 3 : 4, find the three angles.

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