Question

The measure of the angles of a triangle are in the extended ratio of 3 : 7 : 10. Find the measures of the angles.

A. 27 degrees, 63 degrees, 90 degrees
B. 30 degrees, 60 degrees, 90 degrees
C. 30 degrees, 70 degrees, 100 degrees
D.33 degrees, 77 degrees, 80 degrees

Answer 1

The measure of the angles of a triangle are in the extended ratio of 3 : 7 : 10. Find the measures of the angles.

A. 27 degrees, 63 degrees, 90 degrees✓

B. 30 degrees, 60 degrees, 90 degrees

C. 30 degrees, 70 degrees, 100 degrees

D.33 degrees, 77 degrees, 80 degrees

A. is the right answer.

Explanation:

Let the required angles of the triangle be 3x, 7x and 10x

According to the above problem,

`3x + 7x + 10x = 180 \\ 20x = 180 \\ x = (180)/(20) \\ \boxed{x = 9}`

Therefore the angles are :---

`3x = 3 * 9 = 27°✓ \\ 7x = 7 * 9 = 63°✓ \\ 10x = 10 * 9 = 90°✓`

Answer 2

A. 27 degrees, 63 degrees, 90 degrees.

Explanation:

Let the angle of the triangle be x

Given the following data;

3 : 7 : 10 = 3x : 7x : 10x

We know that the sum of the sides of a triangle is equal to 180 degrees.

3x + 7x + 10x = 180

20x = 180

x = 180/20

x = 9

For the first side;

3x = 3 × 9 = 27°

For the second side;

7x = 7 × 9 = 63°

For the third side;

10x = 10 × 9 = 90°

Therefore, the ratio of the angles of the triangle is 27° : 63° : 90°.