Question

If three angles of a triangle are in the ratio 2:3:4, find the value of each angle.

Answer 1

Step-by-step explanation:

If the angles of a triangle are in the ratio 2:3:4, what are the angles?

Let’s assume a triangle ABC with angles, <A, <B and <C.

Given, <A : <B : <C is equal to 2:3:4, let’s assume the values of angles as,

<A = 2x

<B = 3x

<C = 4x,

x is a whole number. You can see that we have taken the values of angles such that they are still in the ratio 2:3:4.

Now, we know that the sum of all the angles of a triangle is 180°.

So, in triangle ABC

<A + <B + <C = 180°

Putting values of angles,

2x + 3x + 4x = 180°

9x = 180°

x = 180°/9

x = 20°

So, angles are as follows,

<A = 2(x) = 2(20°) = 40°

<B = 3(x) = 3(20°) = 60°

<C = 4(x) = 4(20°) = 80°

Answer 2

★ How to do :-

Here, we are given with the ratio of three sides of a triangle. We should find the measure of each angle by using the concept of the ratios, sum of all angles property and the transportation method. We know that all the angles of the triangle together when added should result in 180. That is, the sum of all the angles of triangle should measure 180°. So, we can find the measure of all angles by using the correct methods. So, let's solve!!

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➤ Solution :-

${\tt \leadsto 2:3:4 = 180}$

${\tt \leadsto 2x + 3x + 4x = {180}^{\circ}}$

${\tt \leadsto 9x = {180}^{\circ}}$

${\tt \leadsto x = \dfrac{180}{9}}$

${\tt \leadsto \cancel \dfrac{180}{9} = \boxed{\tt x = 20}}$

$\:$

Now,

Measure of first angle :-

${\tt \leadsto 20 \times 2}$

${\tt \leadsto {40}^{\circ}}$

Measure of second angle :-

${\tt \leadsto 20 \times 3}$

${\tt \leadsto {60}^{\circ}}$

Measure of third angle :-

${\tt \leadsto 20 \times 4}$

${\tt \leadsto {80}^{\circ}}$

Hence solved !!

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More to know :-

• The triangle is a 3-sided, 2-D shape. The triangles are classified into three types. They are :-

1. Equilateral triangle :- The triangle in which all the sides are equal are known as an equilateral triangle.
2. Isosceles triangle :- The triangle in which two sides measure the same and the other one side measure is called a isosceles triangle
3. Scalene triangle :- The triangle in which all the sides measure differently is called a scalene triangle.