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Byju's Answer

Standard VI

Mathematics

Equilateral Triangle

Consider the ...

Question

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 $180^{\circ}$ .

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 $180^{\circ}$ . Hence, any number of adjacent angles on a straight line add up to $180^{\circ}$ . Conversely, if adjacent angles add up to $180^{\circ}$ then the angles have to be on a straight line. Hence, 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 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 $180^{\circ}$ .

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.

Q. Statement

1

: If

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

and

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

, then

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

Statement

2

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

Choose the correct option.

Statement $1 : (p \land \sim q) \land (\sim p \land q)$ is a fallacy.

Statement $2 : (p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow\sim p)$ is a tautology.

Q. Statement 1: The number of unpaired electrons in the following ions:

M n^{2 +}, C r^{3 +}, V^{3 +}

and

T i^{3 +}

are 5, 3, 2 and 1 respectively.
Statement 2:

V^{3 +}

has a magnetic moment

(8)^{\frac{1}{2}} B M

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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 $180^{\circ}$ .

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Consider the two statements: Statement 1: The points A, B, and C will lie on a straight line if ∠ABD + ∠CBD = 180∘. Statement 2: The angle on a straight line is 180∘.

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FREE TEXTBOOK SOLUTIONS

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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 $180^{\circ}$ .