Question

The measures of the angle of a triangle are in the ratio of 1:3:6.What is the largest angle?

Answer 1

Solution:

Given:

⇒ The measures of angle of Δ are in the ratio = 1:3:6

To Find:

⇒ Largest angle.

Formula used:

⇒ Side 1 + Side 2 + Side 3 = 180°  [Sum of sides of triangle is 180°]

Now,

Let the sides of triangle be:

⇒ Side 1 = x

⇒ Side 2 = 3x

⇒ Side 3 = 6x

So, x + 3x + 6x = 180°

⇒ 10x = 180°

⇒ x = 180°/10

⇒ x = 18°

So, Sides of triangle are:

⇒ Side 1 = x = 18°

⇒ Side 2 = 3x = 3 × 18 = 54°

⇒ Side 3 = 6x = 6 × 18 = 108°

Verification:

⇒ Side 1 + Side 2 + Side 3 = 180°

⇒ 18° + 54° + 108° = 180°

⇒ 180° = 180°

∴ LHS = RHS

Hence Proved!!

Answer 2

SOLUTION:-

Given:

The measures of the angle of a ∆ are in the ratio of 1:3:6.

To find:

The largest angle.

Explanation:

Triangle: A triangle is a simple closed curve which is created by three line segments.

Let the angle be R.

We have,

• First angle of ∆= R
• Second angle of ∆= 3R
• Third angle of ∆= 6R

We know that, sum of three angle of a triangle = 180°.

Therefore,

=) R + 3R+ 6R= 180°

=) 10R= 180°

=) R= 180°/10

=) R= 18°

Now,

• 1st angle,R=18°
• 2nd angle,3R=3×18°= 54°
• 3rd angle,6R= 6×18= 108°

108° is the largest angle of the triangle.