(a) In the given figure, prove that lines lm & nq are parallel to each other. [3 MARKS]

(b) What is the value of "x” if AB is parallel to CD in the figure?

Open in App

Solution

(a) Steps: 1 Mark
Proof: 1 Mark
(b) Solution: 1 Mark

(a) Given, $∠ l s t = 105^{\circ}$ and $∠ n t s = 75^{\circ}$

$∠ l s t + ∠ n t s = 105^{\circ} + 75^{\circ} = 180^{\circ}$

But these are co-interior angles

Since co-interior angles are supplementary, lines are parallel

Hence, the lines lm and qn are parallel.

(b) Since AB is parallel to CD, corresponding angles will be equal.

Therefore, x = 130°

Suggest Corrections

Similar questions

(a) In the figure shown below, what are the conditions on $∠ N O B$ and $∠ M P C$ that assure that line segment AB is parallel to the line segment CD? [2 MARKS]

(b)

Given line 'm' is parallel to line 'l'. Find x?

(a) In the given figure, the base of the triangle is parallel to line $l$ and $∠ 1 = ∠ 2$ . Prove that line BC & $m$ are parallel to each other.

(b) Consider the following figure. Find the angle y.

[4 MARKS]

Find the value of x, if it is given that lines AB and CD are parallel to each other.

Q. In the Figure, if

L M ∥ C B

and

L N ∥ C D

, prove that

\frac{A M}{A B} = \frac{A N}{A D}

In the given figure, the straight line AB and CD are parallel to each other. If angle

p = 55^{0}

and

q = 43^{0}

then answer the given question.

Find the value of x.

Join BYJU'S Learning Program

(a) In the given figure, prove that lines lm & nq are parallel to each other. [3 MARKS] (b) What is the value of "x” if AB is parallel to CD in the figure?

(a) In the given figure, prove that lines lm & nq are parallel to each other. [3 MARKS]

(b) What is the value of "x” if AB is parallel to CD in the figure?