Question

the angle of a triangle are in ratio 5:4:3 find the three angle

Answer 1

Let all angels be - 5x,4x and 3x

5x+4x+3x= 180° (ANGLE SUM PROPERTY)

12x=180°

x=180/12= 15°

All angles are as follows: 5x15= 75, 4x15= 60, 3x15= 45

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Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

The one angle is 75° , second angle is 60° and third angle is 45°

$\textbf{\underline{\underline{Explanation :- }}}$

Given :

The ratio of the angles = 5:4:3

To find :

The measures of all 3 angles.

Solution :

Consider the 3 angles as 5x , 4x and 3x

As we know the property of triangle which is -

$\star$ Angles sum property of Triangle :

This property of triangle says that all Angles in a triangle sum up and make 180°

Now following the angle sum property :

$\sf{\implies5x + 4x + 3x = 180\degree}$

$\sf{\implies9x + 3x = 180}$

$\sf{\implies12x = 180}$

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

$\sf{\implies \: x = 15}$

${\boxed{\bigstar{\sf\:{x = 15}}}}$

Value of 5x

$\sf{\implies5 \times \: x }$

$\sf{\implies 5 \times 15}$

$\sf{\implies 75}$

${\boxed{\bigstar{\sf\:{One \: angle = 75\degree}}}}$

Value of 4x

$\sf{\implies}4 \times x$

$\sf{\implies}4 \times 15$

$\sf{\implies}60$

${\boxed{\bigstar{\sf\:{Second \: angle = 60\degree}}}}$

Value of 3x

$\sf{\implies}3 \times x$

$\sf{\implies}3 \times 15$

$\sf{\implies}45$

${\boxed{\bigstar{\sf\:{Third \: angle = 45\degree}}}}$

$\therefore$ The one angle is 75° , second angle is 60° and third angle is 45°

$\textbf{\underline{\underline{Verification :-}}}$

Now place the values of the angle values and check if they sum 180°

$\sf{\implies75 + 60 + 45 = 180}$

$\sf{\implies}135 + 45 = 180$

$\sf{\implies}180 = 180$

We got the required answer 180° when we added the angle values.

$\therefore$ The one angle is 75° , second angle is 60° and third angle is 45°