Mathematics
In the figure (ii) given below, it is given that ∠ABC = 40° and AD is a diameter of the circle. Calculate ∠DAC.
Circles
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Answer
Consider △ABC and △ADC,
∠ABC = ∠ADC = 40° (∵ angles in same segment are equal.)
In △ADC,
∠DCA = 90° (∵ angle in semicircle is 90°.)
We know that sum of angles of a triangle is 180°.
⇒ ∠DAC + ∠ADC + ∠DCA = 180°.
⇒ ∠DAC + 40° + 90° = 180°
⇒ ∠DAC + 130° = 180°
⇒ ∠DAC = 180° - 130°
⇒ ∠DAC = 50°.
Hence, the value of ∠DAC = 50°.
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