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Question
From the given figure, the value of x is ______.
Options
75°
90°
120°
60°
Solution
From the given figure, the value of x is 120°.
Explanation:
In ΔABC, ∠CAB + ∠ABC + ∠BCA = 180° ......[Angle sum property of a triangle]
⇒ 25° + 35° + ∠BCA = 180°
⇒ ∠BCA = 180° – 60°
⇒ ∠BCA = 120°
Also, ∠BCA is an exterior angle
∴ ∠BCA = ∠D + y
⇒ y = ∠BCA – ∠D = 120° – 60° ......[∵ ∠D = 60°, given]
⇒ y = 60°
Now, ∠x and ∠y from a linear pair
∴ x + y = 180°
⇒ x + 60° = 180°
⇒ x = 180° – 60° = 120°
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