Mathematics
If O is the center of the circle, find the value of x in the following figure (using the given information) :
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Circles
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Answer
Considering △ACB and △ADB,
∠ACB = ∠ADB = x° (∵ angles in same segment are equal.)
Considering △ACB,
∠ABC = 90° (∵ angle in semicircle is 90°.)
Since sum of angles in a triangle is equal to 180°.
⇒ ∠BAC + ∠ACB + ∠ABC = 180°.
⇒ 40° + x° + 90° = 180°
⇒ x° + 130° = 180°
⇒ x° = 50°.
Hence, the value of x = 50°.
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