Question

In Fig. 9.49, if l1 || l2, the value of x is
A. 22 1/2
B. 30
C. 45
D. 60

Answer 1

X =45°

Given:

In Fig. 9.49, if l1 || l2

Find:

The value of x.

Explanation:

• If two lines are parallel to each other and other line is intersecting then sum of angles between the line of same side should be 180 degree.

• That is from  figure.

               a+a+b+b =180 °

                  2(a+b) = 180°

             (a+b) = $\frac{180}{2}$ =90°

• From given figure sum of angles of tangle = 180°
• consider third angle of tangle is y°
• so from property of tangle,

                       y° +  (a+b) = 180°

                                   y° = 180-90 =90°

• From property of line,

                              x + x + y = 180°

                                2 × x = 180-90 =90°

                                     X =45°

To learn more...

1. Difference between plane trigonometry and spherical trigonometry

https://brainly.in/question/1971602

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Answer 2

The value of x is C. 45°

Step-by-step explanation:

From question, l₁ || l₂

From diagram, PQ cuts the parallel lines.

∠DPQ + ∠PQE = 180°

The above equation is consecutive interior angles.

a + a + b + b = 180°

2 (a + b) = 180°

⇒ a + b = 90° → (equation 1)

In ΔAPQ, we get,

∠PAQ + a + b = 180°

∠PAQ = 90°

∠PAQ + x + x = 180° (which is linear pair)

90° + 2x = 180°

2x = 180° - 90°

2x = 90°

∴ x = 45°