Question

Q13. The angles of a triangle are in ratio 4: 6: 8. Find the measure of all the angles of the triangle.​

Answer 1

The measure of all the three angles are :

• The first angle = 40°
• The second angle = 60°
• The third angle = 80°

Given :

• The ratio of the angles of a triangle = 4 : 6 : 8.
• The measure of all the angles of the triangle.

To Find :

• The measure of all the angles of the triangle.

Solution :

Let,

The first angle of a triangle = 4x.

The second angle of a triangle = 6x.

The third angle of a triangle = 8x.

We know that,

All the angles of the triangle is 180°

$: \implies \rm4x + 6x + 8x = 180 \degree \\ \\ : \implies \rm10x + 8x = 180 \degree \\ \\ : \implies18x = 180 \degree \\ \\ : \implies \rm x = \cancel\frac{180 \degree}{18} \\ \\ : \implies \rm x = 10 \degree \\ \\ \: \: \: \therefore \: \: \rm x = 10 \degree \\ \\ \sf So, \: the \: measure \: of \: all \: angles \: are : \\ \\ \bullet \: \: \sf The \: first \: angle = 2x = 4 \times 10 \degree = 40 \degree \\ \bullet \: \: \sf The \: second \: angle = 6x = 6 \times 10 \degree = 60 \degree \\ \bullet \: \: \sf The \: third \: angle = 8x = 8 \times 10 \degree = 80 \degree$

Hence,

The measure of the all the three angles of the triangle are 40°, 60° and 80°.

Answer 2

Answer:

$4x + 6x + 8x = 180 \\ \\ = > 18x = 180 \\ \\ = > x = \frac{180}{18} = 10$

HENCE THERE FORE ANGLES ARE:

4×10=40°

6×10=60°

8×10=80°