Question

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

Answer 1

Answer:

A. 27 degrees, 63 degrees, 90 degrees.

Step-by-step 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°.

Answer 2

Answer:

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.

Step-by-step explanation:

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

According to the above problem,

$3x + 7x + 10x = 180 \\ 20x = 180 \\ x = \frac{180}{20} \\ \boxed{x = 9}$

Therefore the angles are :---

$3x = 3 \times 9 = 27°✓ \\ 7x = 7 \times 9 = 63°✓ \\ 10x = 10 \times 9 = 90°✓$