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Q.

In the figure, which one of the following is not true?

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a

∠ 1 + ∠ 5 = 180^{o}

b

∠ 2 + ∠ 5 = 180^{o}

c

∠ 3 + ∠ 8 = 180^{o}

d

∠ 2 + ∠ 3 = 180^{o}

answer is D.

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Detailed Solution

The given figure is,
Question Image

Question Image

The important properties of supplementary angles are below.
The two angles are said to be supplementary angles when they add up to 180°.
The two angles together make a straight line, but the angles need not be together.
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.
They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are coplanar at separate points.

PQ

parallel to

RS

and line

l

is a transversal.

∴ ∠ 2 + ∠ 5 = 180^{0} . . . . . . . . . .

(1) (co-interior angles are also supplementary angles)

∠ 3 + ∠ 8 = 180^{0} . . . . . . . . . . . . .

(2) ( co-interior angles also upplementary angles)

∠ 1 = ∠ 2 . . . . . . . . . . . . . . . . . .

(3) (Vertically opposite angles)

∴ ∠ 1 + ∠ 5 = 180^{o}

( by equation (1) and (3))

∠ 2 = ∠ 3

(alternate interior angles)
However,

∠ 2 + ∠ 3 = 180^{o}

is not true.
Therefore, option 4 is the right answer.

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In the figure, which one of the following is not true?