A cyclic quadrilateral ABCD is drawn in a circle with centers O, A, and C joined to O. If ∠ABC = 2p and ∠ADC = 3p, what is the measure (in degrees) of the (reflex ∠AOC + ∠ADC)?
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Correct answer: D
Explanation
The correct answer is Option 4 i.e. 252°.
Given,
⇒ ∠ABC = 2P
And ∠ADC = 3P
⇒ ∠ABC+ ∠ADC = 180° (Opposite Angles of Cyclic quadrilateral)
⇒ 2P + 3P = 180°
⇒ 5P = 180°
⇒ P = 36°
Now, ∠ABC = 72° and ∠ADC = 108°
Thus, ∠AOC = 2 × ∠ABC
⇒ ∠AOC = 2 × 72 = 144°
⇒ ∠AOC (Reflex) = 360° - 144° = 216°
Required sum = reflex ∠AOC + ∠ADC
⇒ 144 + 3P
⇒ 144 + 2 × 36 = 144° + 108° = 252°