Question

The angles of a triangle measure (x+10)° , (x+20)° , and (x+30)° . Find the measure of the smallest angle.(1 point)
Responses

50°
50 degrees

70°
70 degrees

40°
40 degrees

60°

Pls be right

Answer 1

To find the angles of the triangle, we start with the given measures:

1. Angle 1: \((x + 10)^\circ\)
2. Angle 2: \((x + 20)^\circ\)
3. Angle 3: \((x + 30)^\circ\)

The sum of the angles in a triangle is always \(180^\circ\). Therefore, we can set up the equation:

\[
(x + 10) + (x + 20) + (x + 30) = 180
\]

Combining like terms gives us:

\[
3x + 60 = 180
\]

Next, we can solve for \(x\):

\[
3x = 180 - 60
\]
\[
3x = 120
\]
\[
x = 40
\]

Now, we can substitute \(x\) back into the expressions for the angles:

1. Angle 1: \(x + 10 = 40 + 10 = 50^\circ\)
2. Angle 2: \(x + 20 = 40 + 20 = 60^\circ\)
3. Angle 3: \(x + 30 = 40 + 30 = 70^\circ\)

The angles of the triangle are \(50^\circ\), \(60^\circ\), and \(70^\circ\).

The smallest angle is \(50^\circ\).

So, the measure of the smallest angle is \( \boxed{50^\circ} \).