Question

the triangle are in the ratio2:3:5.
the difference between the largest angle and the smallest angle is​

Answer 1

$\huge{ \red { \fbox{answer}}}$

• Let the angles be 2x, 3x, 4x

we know,

• Sum of interior angles = 180°

$= > 2x + 3x +4x = 180 \\ \\ = > 9x = 18 0 \\ \\ = > x = 180 \div 9 \\ \\ = > x = 20$

• Now,

Largest angle = 4x = 80°

Smallest angle = 2x = 40

Difference = 80 - 40

= 40°

• hope this helps!!

Answer 2

Correct Question :-

• The angles of a triangle are in the ratio 2 : 3 : 5. Find the difference between the largest angle and the smallest angle.

Answer :-

• The difference between the largest angle and the smallest angle is 54°.

Given :-

• The angles of the triangle are in the ratio 2 : 3 : 5.

To find :-

• The difference between the largest and the smallest angle.

Step-by-step explanation :-

• Here, it has been given that the angles of a triangle are in the ratio 2 : 3 : 5. We have to find the difference between the largest angle and the smallest angle.

• To find the difference between the largest angle and the smallest angle, we first have to find the measures of all the angles. Then we can identify the largest and the smallest angle and find their difference.

• The angles of the triangle are in the ratio 2 : 3 : 5, so let the angles be 2x, 3x and 5x respectively.

We know that :-

$\underline{ \boxed{\sf Sum \: of \: all \: angles \: in \: a \: triangle = 180^{\circ}}}$

• So, the sum of 2x, 3x and 5x must be equal to 180°.

--------------

$\rm \longmapsto 2x + 3x + 5x = 180^{\circ}$

Adding 2x, 3x and 5x,

$\rm \longmapsto 10x = 180^{\circ}$

Transposing 10 from LHS to RHS, changing it's sign,

$\rm \longmapsto x = \dfrac{ \: 180^{\circ}}{10}$

Dividing 180° by 10,

$\overline{\boxed{\longmapsto \rm x = 18^{\circ}}}$

• The value of x is 18°.

--------------

So, all the angles are as follows :-

$\implies\bf2x = 2 \times 18^{\circ} = 36^{\circ}.$

$\implies\bf3x = 3 \times 18^{\circ} = 54^{\circ}.$

$\implies\bf5x = 5 \times 18^{\circ} = 90^{\circ}.$

We see that :-

$\boxed{\sf 36^{\circ} \: is \: the \: smallest \: angle \: here.}$

$\boxed{\sf90^{ \circ} \: is \: the \: largest \: angle \: here.}$

• So, the smallest angle is 36° and the largest angle is 90°.

--------------

Now, the difference between the largest angle and the smallest angle is :-

$\mid \boxed{ \tt90^{ \circ} - 36^{ \circ} = 54^{ \circ}} \mid$

• Hence, the difference between the largest and the smallest angle is 54°.