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Question
In the given figure, if l1 || l2, the value of x is
Options
\[22\frac{1}{2}\]
30
45
60
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Solution
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°
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