Question

In a triangle, If the second angle is 5° greater than the first angle and the third angle is 5° greater than second angle, find the three angles of the triangle. Let x be the first angle.

Answer 1

In a triangle, the first angle is 55°, the second angle is 60°, and the third angle is 65°.

Step-by-step explanation:

Let's assume the first angle is x. According to the problem, the second angle is 5° greater than the first angle, so the second angle is x + 5°. Similarly, the third angle is 5° greater than the second angle, so the third angle is (x + 5°) + 5° = x + 10°.

Since the sum of the angles in a triangle is always 180°, we can form an equation: x + (x + 5°) + (x + 10°) = 180°.

Simplifying the equation, we get 3x + 15° = 180°. Solving for x, we subtract 15° from both sides: 3x = 165°. Dividing both sides by 3, we find that x = 55°.

Therefore, the three angles of the triangle are:
First angle: 55°
Second angle: 55° + 5° = 60°
Third angle: 60° + 5° = 65°

Learn more about Triangle angles