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Question
In the given figure, what is the value of x?
Options
35
45
50
60
Solution
In the given figure, we need to find the value of x.
Here, DBA is a straight line, so using the property, “angles forming a linear pair are supplementary”, we get,
∠CBA + ∠CBD = 180°
7y + 5y = 180°
12y = 180°
`y = (180°)/12`
y = 15°
Now, applying the value of y in ∠CBA and ∠BCA
∠BCA = 3y
= 3(15°)
= 45°
Also,
∠CBA = 5y
= 5(15°)
= 75°
Further, applying angle sum property of the triangle
In ΔABC
∠A + ∠B +∠C = 180°
x + 75° + 45° = 180°
x + 120°= 180°
x = 180° - 120°
x = 60°
Thus, x = 60°
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