Question

The ratio of the measures of the measures of the angles of a triangle is 2 : 3 : 5 . Find the measure of the smallest angle of the triangle.

Answer 1

Answer:

The smallest angle of the triangle is 36°.

Step-by-step explanation:

The angle sum property of a triangle = 180°

The ratio of the measures of the angles of a triangle = 2 : 3 : 5

= 2x+3x+5x = 10x

➡ 2/10 × 180° = 36 degree

➡ 3/10 × 180° = 54 degree

➡ 5/10 × 180° = 90 degree

36° < 54° < 90°

Therefore, the smallest angle of the triangle is 36°.

Answer 2

Required Answer :

$the \: smallest \: angles \: of \: this \: triangle \: = 36°$

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Step by step explanation : ⤵️

Given :

. Ratio of measure of three angles of triangle are : 2:3:5

To find :

. Measure of smallest angle of this given triangle.

Explanation :

➝ Before finding our answer, We have to Find out the measure of all angles.

Let the angles of this triangle = 2x, 3x And 5x

Now,

we can say that ,

2x + 3x + 5x = 180° ---( sum of interior angle of triangle= 180°)

HENCE, Solve this equation =

2x + 3x + 5x = 180°

=> 10x = 180°

=> x = 180/10

=> x = 18°

So, We have the value of x = 18°

Now, We can find out the measure of all angles of triangle by putting the value of x in it.

. 2x

➝ 2 × 18 = 36°

so, the one Angle of this triangle = 36°

. 3x

➝ 3 × 18 = 54°

so, second Angle = 54°

. 5x

➝ 5 × 18 = 90°

so, third angle = 90°

Hence,

The measure of all angles of triangle are as :-

36° , 54° , 90°

Now,

question asked to find smallest angle of triangle.

So,

in this solution, We can see that the smallest angle is 36°

so,

Answer :- 36°