Q71 of 93 Page 6

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

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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69 (v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.   70 Fill 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 …………. 72 If the angles of a triangle are in the ratio 2 : 3 : 4, find the three angles. 73 Prove that if one angle of a triangle is equal to the sum of the other two angles, the triangle is a right angled.