Q72 of 93 Page 6

If the angles of a triangle are in the ratio 2 : 3 : 4, find the three angles.

Let the three angles be 2x, 3x and 4x.2x + 3x + 4x = 180° (The sum of three angles a triangle is 180° )                 9x = 180°                   x = = 20°∴ The three angles are 2 × 20°, 3 × 20°, 4 × 20°i.e. The three angles are 40°, 60° and 80°.

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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 …………. 71 One of the angles of a triangle is 65°. Find the remaining two angles, if their difference is 25°. 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. 74 An exterior angle of a triangle is 115° and one of the interior opposite angles is 35°. Find the other two angles.