Question

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Answer 1

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Given :-

• m || n

To find :-

• ∠ACB

Construction :-

⟼Through C, draw a line 'p' parallel to m.

$\bf \: ⟼ p || m || n$

$\begin{gathered}\Large{\bold{\red{\underline{CaLcUlAtIoN\::}}}} \end{gathered}$

$\bf \: ⟼ As \: p || m$

$\bf \: ⟼  ∠a \: = ∠x \: ⟼ \: (1)$

[ By alternate Interior Angles]

⟼Again,

$\bf \: ⟼ As \: p || n$

$\bf \: ⟼ ∠b = ∠y \: ⟼ \: (2)$

⟼ On Adding equation (1) and (2), we get

$\bf \: ⟼ ∠x + ∠y = ∠a + ∠b$

$\bf \: ⟼ ∠ACB = ∠x + ∠y$

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What are Parallel Lines?

• When the distance between a pair of lines is always the same, then we call such lines as parallel lines. The symbol for “parallel to” is “// “. Parallel lines are the lines which never meet each other. For the two lines to be parallel, the most important thing is that they are drawn in the same plane. These lines are always equidistant from each other.

What is a Transversal?

• A transversal is a line that passes through two lines lying in the same plane at two distinct points. 

Properties of Transversal

• A pair of parallel lines is intersected by a transversal. Following are the properties:

• Vertically opposite angles are equal.

• Corresponding angles are equal.

• The interior angles formed on the same side of the transversal are supplementary.

• Alternate angles are equal.

Answer 2

Answer:

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