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)${75}^{\circ }$

smakkie8iz

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,
$3x+4x+5x={180}^{\circ }$
$⇒12x={180}^{\circ }$
$⇒x=\frac{{180}^{\circ }}{12}$
$⇒x={15}^{\circ }$
Thus,
Smallest angle =3x
$=3×{15}^{\circ }$
$={45}^{\circ }$

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