Question

14. The ratio of the measures of the
three angles of a triangle is 2:3:4.
The measure of the largest angle is
*​

Answer 1

The angles of a triangle are in ratio 2:3:4. What is the measure of each angle of the triangle?

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

Given that,

• The ratio of the measures of the three angles of a triangle is 2:3:4.

☯ Let the three angles be 2x, 3x & 4x.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀

$\dag\;{\underline{\frak{We \ know \ that,}}}$⠀

• Sum of the measures of all angles of triangle is 180°.

⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀

$:\implies\sf 2x + 3x + 4x = 180 \\\\\\:\implies\sf 9x = 180 \\\\\\:\implies\sf x = \cancel\dfrac{180}{9}\\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 20^{\circ}}}}}}$

⠀⠀⠀⠀

Hence,

• First angle, 2x = 2(20) = 40°
• Second angle, 3x = 3(20) = 60°
• Third angle, 4x = 4(20) = 80°

$\therefore\:{\underline{\sf{Hence,\: The \ measure \ of \ the \ largest \ angle \:is\: \bf\pink{80^{\circ}}.}}}$