Question

The angles of a triangle are in the ratio 4 : 2 : 6, the smallest angle of this triangle is

Answer 1

Answer:

☯️For finding the smallest angle, firstly we have to find the angles of triangle.

Let the angles to be 4x, 2x and 6x.

Sum of all angles of triangle = 180°

A.T.Q

4x + 2x + 6x = 180°

12x = 180°

x = 180°/12

x= 15

➡️First angle of triangle = 4×15

= 60°

➡️Second angle of triangle = 2×15

= 30°

➡️Third angle of triangle = 6×15

= 90

So,the smallest angle of triangle is 30°.

♥️hope it will help you.♥️

Answer 2

Answer :-

• The smallest angle of this triangle is 30°.

Given :-

• The angles of a triangle are in the ratio 4 : 2 : 6.

To find :-

• The smallest angle of this triangle.

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Let's understand!

To find the smallest angle of the triangle, we first have to find the value of all the angles using the ratio given. We will also use the angle sum property. And at last, we will compare the angles and find the smallest one.

How to solve?

We know that :-

Sum of all the angles in a triangle = 180°.

Therefore, let's use this property to find all the angles.

Calculations :-

Since the angles are in the ratio 4 : 2 : 6, then let them be 4x, 2x and 6x respectively.

They are the angles of a triangle, so they must add up to 180°.

Therefore, let's construct an equation using this information.

We get :-

$\sf4x + 2x + 6x = 180$

Adding all the variables,

$\sf12x = 180$

Transposing 12 from LHS to RHS, changing it's sign,

$\sf x = \dfrac{180}{12}$

Dividing 180 by 12,

$\sf x = 15.$

The value of x is 15.

So, the value of the angles are as follows :-

4x = 4 × 15 = 60°.

2x = 2 × 15 = 30°.

6x = 6 × 15 = 90°.

It's clear that 30° is the smallest angle here.

Thus, 30° is the smallest angle of this triangle.

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