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Linear Pair

With referenc...

Question

With reference to the figure below, consider the two statements:

Statement 1: The points A, B, and C will lie on a straight line if x + y = $180^{\circ}$ .

Statement 2: The angle on a straight line is $180^{\circ}$ .

Both the statements are true and statement 2 is the correct explanation of statement 1

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Both the statements are true and statement 2 is not the correct explanation of statement 1

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Statement 1 is true and Statement 2 is false

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Statement 1 is false and statement 2

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Solution

The correct option is A
Both the statements are true and statement 2 is the correct explanation of statement 1

The angle on a straight line is $180^{\circ}$ . Adjacent angles on a straight line add up to $180^{\circ}$ .

Conversely, if adjacent angles add up to $180^{\circ}$ then the angles are on a straight line.

Hence, if x + y = $180^{\circ}$ , then A, B and C lie on a straight line.

Therefore, both the statements are true and statement 2 is the correct explanation of statement 1.

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Similar questions

With reference to the figure below, consider the two statements:

Statement I: The points A, B, and C will lie on a straight line if x + y = $180^{\circ}$ .

Statement II: If the angle between two lines is $180^{\circ}$ , then all the points on both the lines lie on a straight line.

Consider the two statements:

Statement 1: The points A, B, and C will lie on a straight line if $∠ A B D$ + $∠ C B D$ = $180^{\circ}$ .

Statement 2: The angle on a straight line is $180^{\circ}$ .

1

\to A = 2^i + 3^j + 6^k, \to B =^i +^j - 2^k

\to C =^i + 2^j +^k

| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = 243

2

| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = | \to A |^{2} | [\to A \to B \to C] |

4^{\circ} C

Statement 1:

(\sqrt{- 3 + 4 x - x^{2}} + 4)^{2} + (x - 5)^{2}

1 \leq x \leq 3)

36.

Statement 2:

(5, - 4)

(x - 2)^{2} + y^{2} = 1

6

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