Question

In Fig. 9.47, for which value of x is l1 || l2?
A. 37
B. 43
C. 45
D. 47

Answer 1

For x=47, L1 || L2

Solution: If L1 || L2,

<PBA=<BAQ ( Alternate interior

angles)

=>78°=<BAC+<CAQ

=>78°=<BAC+35°

=><BAC = 43°

Now , In triangle ABC

=> <BAC+<ABC+<BCA = 180° (Angle

sum property of triangle)

=>43°+×°+90°=180°

=>x°+133°=180°

=>x=47°

Answer 2

Option D: The value of x is 47°

Explanation:

Given that $l_{1} \| l_{2}$

We need to find the value of x.

Let us apply the property that, "if two lines are parallel then the alternate interior angles are equal",

Thus, applying the above property, we have,

    $78^{\circ}=35^{\circ}+\angle C A B$

$\angle C A B=78^{\circ}-35^{\circ}$

$\angle C A B=43^{\circ}$

Let us consider the triangle ABC

By angle sum property, we have,

$\angle C A B+\angle A C B+\angle C B A=180^{\circ}$

Substituting the values, we have,

$43^{\circ}+90^{\circ}+x=180^{\circ}$

                  $x=180^{\circ}-133^{\circ}$

                  $x=47^{\circ}$

Thus, the value of x is 47°

Therefore, Option D is the correct answer.

Learn more:

(1) In the figure, for what value of x is l1 parallel to l2

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(2) In fig l1 parallel to l2 and a1 parallel to a2. find the value of x

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