Two angles whose sum, is $180^{\circ}$ are called supplementary angles. Four angles are formed at the intersection of two lines. How many pairs of supplementary angles and equal angles are formed?

Two pairs of supplementary and one pair of equal angles.

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Two pairs of each.

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One pair of supplementary and two pairs of equal angles.

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Four pairs of supplementary and two pairs of equal angles.

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Solution

The correct option is D
Four pairs of supplementary and two pairs of equal angles.

Consider two lines intersecting as shown.

At the intersection of two lines, sum of angles on one side of a line is $180^{\circ}$ . Consider 'line 1', on one side lies angles 'a' and 'd', and on the other side lies 'b' and 'c'. Similarly, consider 'line 2', on one side we have angles 'a' and 'b', and on the other side we have 'd' and 'c'.

So, totally we have four pairs of supplementary angles

a & d,

b & c,

a & b

'd' & 'c'.

Secondly, opposite angles are equal at the intersection of two lines. Here 'a & c' and 'b & d' are opposite pairs, and they are equal. So, there are two pairs of equal angles.

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Similar questions

Statement $1$ : When two lines intersect each other, only the angles forming linear pair are supplementary.

Statement $2$ : When two lines intersect each other, angles forming linear pair are supplementary.

Choose the correct option.

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 _______.

Q. angles formed when a transversal intersects two parallel lines are supplementary

Q. Two angles are equal and they form a pair of supplementary angles. Find their magnitude.

Consider the following statements:
When two straight lines intersect:
(i) adjacent angles are complementary
(ii) adjacent angles are supplementary
(iii) opposite angles are equal
(iv) opposite angles are supplementary

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Two angles whose sum, is 180∘ are called supplementary angles. Four angles are formed at the intersection of two lines. How many pairs of supplementary angles and equal angles are formed?

Two angles whose sum, is $180^{\circ}$ are called supplementary angles. Four angles are formed at the intersection of two lines. How many pairs of supplementary angles and equal angles are formed?