in the given figure O is the centre of the circle and angle BOC = 130° find measure of angle ADC
Answers
Step-by-step explanation:
/_COB + /_COA = 180° (Linear pair)
130° + /_COA = 180°
/_COA = 180° - 130°
/_COA = 50°
Now, /_ADC = 1/2 × /_COA (angle subtended by an arc at the centre is double the angle subtended by an arc on circumference)
/_ADC = 1/2 × 50° = 25°.
The measure of ∠ADC is 325°.
Since O is the center of the circle, the line segment OC is a radius of the circle. Similarly, line segment OA is also a radius of the circle. Thus, we have:
∠BOC = 130° (Given)
∠AOC = 2∠BOC = 2(130°) = 260° (Angle at the center is twice the angle at the circumference)
∠AOD = 180° - ∠AOC = 180° - 260° = -80° (Angle sum of a straight line)
∠BOD = ∠BOC/2 = 130°/2 = 65° (Angle at the center is twice the angle at the circumference)
∠COD = ∠AOD - ∠BOD = -80° - 65° = -145°
Note that ∠COD is a negative angle since it is measured clockwise from line segment OC. To find the measure of ∠ADC, we need to find the supplement of ∠COD, which is a positive angle. The supplement of ∠COD is given by:
180° - |∠COD| = 180° - |-145°| = 180° + 145° = 325°
Therefore, the measure of ∠ADC is 325°.
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