Question

32
If the measures of angles of a triangle are in the ratio 3:4:5, what is the measure of the smallest
angle of the triangle?
k
O 25°
O 30°
45°
60°​

Answer 1

Answer :

• 45⁰ is the measure of the smallest angle of a triangle

Given :

• The measure of angles of a triangle are in the ratio 3 : 4 : 5

To find :

• Smallest angle of triangle

Solution :

• Let the ratio be 3x , 4x and 5x

As we know that,

• Sum of all angles in a triangle is equal to 180⁰

According to question,

》3x + 4x + 5x = 180⁰

》12x = 180⁰

》x = 180⁰/12

》x = 15

Now we have to find the smallest angle of a triangle:

• 3x = 3(15) = 45⁰
• 4x = 4(15)= 60⁰
• 5x = 5(15) = 75⁰

Hence , 45⁰ is the measure of the smallest angle of a triangle

Answer 2

$\huge\frak{\underline{\red{Given:}}}$

• The measures of angles of a triangle are in the ratio 3:4:5.

$\huge\frak{\underline{\red{To\:Find:}}}$

• The measure of the smallest angle of the triangle.

$\huge\frak{\underline{\red{Solution:}}}$

Let the angles of the triangle be 3x,4x and 5x

$\large\:\:\:\:\:\:{\boxed{\sf{\orange{★Angle\:Sum\:Property_{(traingle)} :the\:sum\:of\:all\:angles\: in\:a\: triangle\:is\:180^{\circ}}}}}$

Therefore,

$\longrightarrow{\sf{3x+4x+5x=180^{\circ}}}$

$\longrightarrow{\sf{12x=180^{\circ}}}$

$\longrightarrow{\sf{x= \dfrac{180^{\circ}}{12}}}$

$\longrightarrow{\boxed{\sf{x=15}}}$

So, the angles will be :

$\longrightarrow{\boxed{\sf{3x=3\times 15 = 45}}}$

$\longrightarrow{\boxed{\sf{4x=4\times 15 = 60}}}$

$\longrightarrow{\boxed{\sf{5x=5\times 15 = 75}}}$

Hence, we can see that the smallest angle is 45°.

So our answer will be $\huge{\boxed{\mathbf{\pink{45^{\circ}}}}}$

__________________________

Note : please see the answer from brainly web.