In the adjoining figure, O is the center of a circle. If angle ∠DAC = 25°, find the values of angle ∠BDC and angle ∠BAC.
1 Answer
Given:
O is the center of the circle
and ∠DAC = 25°
To find:
The values of the angles ∠BDC and ∠BAC
Here,
- ∠DBC = ∠DAC = 25° [ being angles inscribed in the same segment of a circle ]
- ∠BCD = 90° [ being angle inscribed in a semi-circle]
- ∠DBC + ∠BCD + BDC = 180° [ sum of the interior angles of a triangle BCD]
Or, 25° + 90° + ∠BDC = 180°
Or, ∠BDC = 180° - 115°
Or, ∠BDC = 65° - ∠BAC = ∠BDC = 65° [ being angles inscribed in the same segment of a circle ]
∴ ∠BDC = 65° and ∠BAC = 65° is the required answer
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