In the following figure, a transversal c intersects two parallel lines a and b at A and B respectively and the angles formed at A and B are marked. Tell which of the following pairs of angles need not be equal?
(a) ∠1, ∠2
(b) ∠1, ∠3
(c) ∠1, ∠5
Answers
ANGLES
Given:
Two parallel lines 'a' and 'b' which are intersected by a transversal 'c.' Angles formed are at A and B.
To Find:
Which pair of angles given in the options need no to be equal?
Solution:
The given pair of angles are:
(a) ∠1, ∠2
(b) ∠1, ∠3
(c) ∠1, ∠5
If we look at the figure carefully, then we can make the following observations:
(a) ∠1 and ∠2 forms a Linear Pair. When two lines gets intersected, then two adjacent angles formed due to intersection forms a linear pair. The sum of both the angles is equal to 180° as the angles formed are on straight line. Two angles which form a linear pair can only be equal when they both are 90° each, otherwise they can be unequal as well.
(b) ∠1 and ∠3 are Vertically Opposite Angles (V.O.A.). When two lines intersect with each other then the opposite angles formed are called Vertically Opposite Angles. They are always equal.
(c) ∠1 and ∠5 are Corresponding Angles. A line which gets cut by two transversals at two different points, then the pair of angles which are at the same positions of the transversals are known as corresponding angles. They are always equal.
After making the above observations and statements, we can clearly say that Option (a) ∠1, ∠2 need not be equal. There measure can be anything which sums up to 180°. Example: 110° and 70°, 100° and 80°, 60° and 120° etc.
Final Answer:
Option (a) ∠1, ∠2 is the correct answer.
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