Write the converse of each of the following statements.

(i) If the sum of measures of angles in a figure is 180⁰ , then the figure is a triangle.

(ii) If the sum of measures of two angles is 90⁰ then they are complement of each other.

(iii) If the corresponding angles formed by a transversal of two lines are congruent then the two lines are parallel.

(iv) If the sum of the digits of a number is divisible by 3 then the number is divisible by 3.

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Solution

(i) If the given figure is a triangle, then the sum of the measures of its angles is 180⁰.

(ii) If the given two angles are complement of each other, then the sum of the measures of two angles is 90⁰.

(iii) If the given two lines are parallel, then the corresponding angles formed by a transversal of two lines are congruent.

(iv) If the given number is divisible by 3, then the sum of the digits of the number is divisible by 3.

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Similar questions

Select the correct alternative and fill in the blanks in the following statements.

(i) If a transversal intersects two parallel lines then the sum of interior angles on the same side of the transversal is ............

(A) 0^° (B) 90^°(C) 180^° (D) 360^°

(ii) The number of angles formed by a transversal of two lines is ............

(A) 2 (B) 4 (C) 8 (D) 16

(iii) A transversal intersects two parallel lines. If the measure of one of the angles is 40^∘ then the measure of its corresponding angle is .............

(A) 40^°(B) 140^° (C) 50^° (D) 180^°

(iv) In

∆

ABC,

∠

A = 76^° ,

∠

B = 48^°,

∴

C = ..............

(A) 66 ° (B) 56 ° (C) 124 ° (D) 28 °

(v) Two parallel lines are intersected by a transversal. If measure of one of the alternate interior angles is 75^° then the measure of the other angle is .............

(A) 105^° (B) 15^° (C) 75^° (D) 45^°

Q. Fill in the 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) Two lines parallel to the same line are ... to each other.
(v) If a transversal intersects a pair of lines in such away that a pair of alternate angles are equal, then the lines are ...
(vi) If a transversal intersects a pair of lines in such away that the sum of interior angles on the same side of transversal is 180°, then the lines are ...

Q. Write the convese of the following statement
" If the sum of measures of two angles is

180^{o}

, then they are supplementary of each other"

Fill in the blanks:

(i) If two angles are complementary, then the sum of their measures is _______.

(ii) If two angles are supplementary, then the sum of their measures is _______.

(iii) Two angles forming a linear pair are _______.

(iv) If two adjacent angles are supplementary, they form a _______.

(v) If two lines intersect at a point, then the vertically opposite angles are always _______.

(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are _______.

If two lines are intersected by a transversal, then each pair of corresponding angles so formed is :

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