Question

Calculate the angles of a triangle if they are in the ratio 3 : 7 : 8.​

Answer 1

Given:

The angles of a triangle in the ratio 3 : 7 : 8.

What to do?

Find the actual angles of a triangle.

How to do?

To find the angles of the triangle we have to take a variable for the common measures as they are in ratio and then use the formula of the sum of interior angles of the triangle which is equal to 180°.

Solution:

Let the common measures be x.

Sum of angles of triangle = 180°  

So the equation will be,

⇒ 3x + 7x + 8x = 180°

Add the terms in LHS,

⇒ 18x = 180°

Take 18 to RHS,

⇒ x = $\frac{180}{18}$

Divide 180 by 18,

⇒ x = 10

Now substitute the values,

• 3x = 3(10) = 30°
• 7x = 7(10) = 70°
• 8x = 8(10) = 80°

To Verify:

3x + 7x + 8x = 180°

Substitute the values in the equation,

⇒ 3(10) + 7(10) + 8(10) = 180°

Remove the brackets and multiply,

⇒ 30° + 70° + 80° = 180°

Add the numbers,

⇒ 180° = 180°

∴ Hence, verified.

Property used:

Sum of the interior angles of triangle = 180°

Answer 2

Answer:

The Angles are

• 30°

• 70°

• 80°

Step-by-step explanation:

GiveN

• The ratio of angles of a Triangle are 3:7:8.

To Find

• The all the angles of the Triangle

SolutioN

• Let us assume the angles of the Triangle be 3x,7x,8x

• We know that Sum of all the angles of the Triangle is 180°[ASP Property]

• So, 3x + 7x , 8x = 180

• 18x = 180

• $\bf x =\frac{ 180}{18}$

• x = 10°

So, The angles of the Triangle are

• 3x = 3 × 10 = 30°

• 7x = 7 × 10 = 70°

• 8x = 8 × 10 = 80°