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The three successive angles of a cyclic quadrilateral are in the ratio 1 : 3 : 4, find the measure of the fourth angle?
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- 72°
- 108°
- 36°
- 30°
- 72°
Correct Option: A
As we know that ,
The sum of opposite angles of a concyclic quadrilateral is 180°.
Given , Ratio = 1 : 3 : 4
∠A : ∠B : ∠C = 1 : 3 : 4
∴ ∠A : ∠C = 1 : 4
| ∠A = | × 180° = 36° | |
| 5 |
| ∠C = | × 180° = 144° | |
| 5 |
∴ ∠B = 3 × 36° = 108°
∴ ∠D = 180° – 108º = 72°
