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In a ∆ABC, if 4∠A = 3 ∠B = 12 ∠C, find ∠A.
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- 22.5°
- 90°
- 67.5°
- 112.5°
- 22.5°
Correct Option: C
As per the given in question ,
∴ 4∠A = 3∠B = 12∠C
{ LCM of 4 , 3 , 12 is 12 }
| ⇒ | = | = | |||
| 12 | 12 | 12 |
| ⇒ | = | = | |||
| 3 | 4 | 1 |
∴ ∠A : ∠B : ∠C = 3 : 4 : 1;
∠A + ∠B + ∠C = 180°
∴ Sum of the terms of ratio = 3 + 4 + 1 = 8
| ∴ ∠A = | × 180° = 67.5° | |
| 8 |
