Question

The second angle of a triangle is 3 times as large as the first angle. The third angle is 30 degrees more than the first angle. Find the measure for the angles

Answer 1

hope this will help u.. :-)

Answer 2

Given,

2nd angle of a triangle is 3 times the 1st angle.

3rd angle is 30 degrees more than the 1st angle.

To find,

The measure of the angles.

Solution,

Firstly, in the given triangle, let the first angle be x.

It is given that the 2nd angle of the triangle is thrice or 3 times the first angle. So,

2nd angle = 3x.

Also, the 3rd angle is 30° more than the first angle. That is,

3rd angle = (x + 30).

As we know that in a triangle, the sum of all the angles is equal to 180°.

Thus, for the given triangle, we have,

(x) + (3x) + (x + 30) = 180

Simplifying the above equation,

5x + 30 = 180

⇒ 5x = 180 - 30

⇒ 5x = 150

⇒ x = 30.

From the above value of x, we can see that for the given triangle,

• 1st angle = x = 30°,
• 2nd angle = 3x = 3·(30) = 90°, and,
• 3rd angle = (x + 30) = (30 + 30) = 60°.

Therefore, the three angles of the triangle are 30°, 60°, and 90°.