Saved Bookmarks
| 1. |
In a ∆ABC, ∠C = 3∠B = 2(∠A + ∠B). Find the measure of each one of ∠A, ∠B and ∠C. |
|
Answer» In a ∆ABC, ∠C = 3∠B = 2(∠A + ∠B). ∴ 3∠B = 2(∠A + ∠B) ⇒ 3∠B = 2∠A + 2∠B ⇒ 3∠B – 2∠B = 2∠A ⇒ ∠B = 2∠A. And ∠C = 3∠B = 6∠A. (∵∠B = 2∠A) We know that sum of angles in a triangle is 180°. ∴ ∠A + ∠B +∠C = 180° ⇒ ∠A + 2∠A + 6∠A = 180° ⇒ 9∠A = 180° ⇒ ∠A = \(\frac{180°}{9}\)= 20°. Now, ∠B = 2∠A = 2× 20° = 40°. And ∠C = 6∠A = 6 ×20° = 120°. Hence, ∠A = 20°, ∠B = 40° and ∠C = 120°. |
|