Rocco May

2023-03-11

The angles of a triangle are in the ratio 3:4:5. Find the smallest angle.

A)${30}^{\circ}$

B)${45}^{\circ}$

C)${60}^{\circ}$

D)${75}^{\circ}$

A)${30}^{\circ}$

B)${45}^{\circ}$

C)${60}^{\circ}$

D)${75}^{\circ}$

smakkie8iz

Beginner2023-03-12Added 5 answers

The correct answer is B: ${45}^{\circ}$

Given that the angles of a triangle are in the ratio 3:4:5.

Let the measure of the angles be 3x,4x,5x.

We know that, the sum of the angles of a triangle =${180}^{\circ}$

Thus,

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

$\Rightarrow 12x={180}^{\circ}$

$\Rightarrow x=\frac{{180}^{\circ}}{12}$

$\Rightarrow x={15}^{\circ}$

Thus,

Smallest angle =3x

$=3\times {15}^{\circ}$

$={45}^{\circ}$

Given that the angles of a triangle are in the ratio 3:4:5.

Let the measure of the angles be 3x,4x,5x.

We know that, the sum of the angles of a triangle =${180}^{\circ}$

Thus,

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

$\Rightarrow 12x={180}^{\circ}$

$\Rightarrow x=\frac{{180}^{\circ}}{12}$

$\Rightarrow x={15}^{\circ}$

Thus,

Smallest angle =3x

$=3\times {15}^{\circ}$

$={45}^{\circ}$