Math, asked by sandeepkkaur55, 1 month ago

8. Calculate the angles of a triangle if they are in the ratio 4:5:6.
9. One angle of a triangle is 60°. The other two angles are in the ratio 6:4. Find the other angles.

Answers

Answered by SparklingThunder

Answer:

$8. \: \: we \: know \: that \: sum \: of \: all \: angles\: of \triangle \: = 180 \degree \\ \therefore \: 4x + 5x + 6x = 180 \degree \\ 15x = 180 \degree \\ x = \frac{180 \degree}{15} \\ x = \frac{ \cancel{180 }\degree}{ \cancel{15}} = 12 \degree \\ 4x = 4 \times 12 = 48 \degree \\ 5x = 5 \times 12 = 60 \degree \\ 6x = 6 \times 12 = 72 \degree \\ \purple{\fbox{ \red{ the \: angles \: of \: triangle \: are \: 48\degree, \: 60\degree \: and \: 72\degree}}}$

$9. \: \: we \: know \: that \: sum \: of \: all \: angles\: of \triangle \: = 180 \degree \\ \therefore \: 4x + 60 \degree + 6x = 180 \degree \\ 10x = 180 \degree - 60 \degree \\ x = \frac{120 \degree}{10} \\ x = \frac{ \cancel{120 }\degree}{ \cancel{10}} = 12 \degree \\ 4x = 4 \times 12 = 48 \degree\\ 6x = 6 \times 12 = 72 \degree \\ \purple{\fbox{ \red{ the \: other \: angles \: of \: triangle \: are \: 48\degree \: and \: 72\degree.}}}$

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Answered by Eutuxia

Question~

Calculate the angles of a triangle if they are in the ratio 4:5:6.

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Given :

Ratios of Angle = 4:5:6

To find :

the angles of a triangle in the ratio of 4:5:6

Solution :

✳ The total angles of a Triangle are 180°.

⇒ Let's find the angles.

4:5:6 = 180°

4x + 5x + 6x = 180°

15x = 180/15

= 12

4x = 4 × 12

= 48°

5x = 5 × 12

= 60°

6x = 6 × 12

= 72°

Therefore, the angles are 48°, 60° and 72°.

Question~

One angle of a triangle is 60°. The other two angles are in the ratio 6:4. Find the other angles.

------------------

Given :

Ratios of Angle = 4:5:6

To find :

the angles of a triangle in the ratio of 4:5:6

Solution :

✳ The total angles of a Triangle are 180°.

⇒ Let's find the angles.

= 180° - 60°

= 120°

6:4 = 120°

4x + 6x = 120°

10x = 120/10