Question

[10] The angles of a triangle are in the ratio 2 : 3: 7. The measure of the
largest angle is​

Answer 1

Given:

• The angles of a triangle are in the ratio 2:3:7.

To find:

• The measure of the largest angle?

Solution:

• Let's consider the angles as 2x,3x & 7x

Where,

• Sum of angles of the triangle = 180°

• Let's take x in common.

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« Now, Forming an equation,

→ 2x + 3x + 7x = 180°

→ 5x + 7x = 180°

→ 12x = 180°

→ x = 180/12

→ x = 15

Therefore, Angles of the triangle are :

• 2x = 15 × 2 = 30°
• 3x = 15 × 5 = 45°
• 7x = 15 × 7 = 105°

∴ Hence, The measure of largest angle is 105°

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« Now, Let's verify this,

→ 2x + 3x + 7x = 180°

→ 5x + 7x = 180°

→ 12x = 180°

→ 12(15) = 180°

→ 180° = 180°

LHS = RHS

• Hence, Verified!

Answer 2

Given :

• The angles of a triangle are in the ratio 2 : 3 : 7 .

To find :

• The measure of the largest angle in the triangle.

Solution :

• Let the angles be 2x , 3x and 7x

According to Angle Sum Property :

➠ 2x + 3x + 7x = 180°

➠ 12x = 180°

➠ x = 180/12

➠ x = 15

Angles :

• 2x = 2 × 15 = 30°
• 3x = 3 × 15 = 45°
• 7x = 7 × 15 = 105°

∴ Required answer :

The measure of the largest angle is 105°

Angle Sum Property :

• Angle Sum Property states that, the sum of all the interior angles in a triangle is always 180°