Question

In the given figure, if l₁ || l₂, the value of x is

Options

• \[22\frac{1}{2}\]

• 30

• 45

• 60

Answer 1

In the given problem,  l₁ || l₂

We need to find the value of x

Here, as l₁ || l₂ , using the property, “consecutive interior angles are supplementary”, we get

∠DAC + ∠ECA = 180°

a + a+ b+ b =180°

2a + 2b = 180°

`a + b = (180°)/2`

 a + b = 90°             ..........(1)

Further, applying angle sum property of the triangle 

In ΔABC

∠BAC + ∠BCA + ∠ABC =180°

              a + b + ∠ABC = 180°

 90 + ∠ABC = 180° (using 1)

∠ABC = 180° - 90°

∠ABC = 90°

Now, AB is a straight line, so using the property, “angles forming a linear pair are supplementary”, we get,

x + x + ∠ABC = 180°

         2x + 90° = 180°

                  2x = 180° - 90°

                   `x = (90°)/2` 

                    x = 45°

Thus, x = 45°