Question

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

Answer 1

To find the measure of the smallest angle in the triangle with angles \((x+10)^\circ\), \((x+20)^\circ\), and \((x+30)^\circ\), we first use the fact that the sum of the angles in a triangle is always \(180^\circ\).

Setting up the equation:

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

Combine like terms:

\[
3x + 60 = 180
\]

Now, solve for \(x\):

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

Now that we have the value of \(x\), we can find the measures of the angles:

1. First angle:
\[
x + 10 = 40 + 10 = 50^\circ
\]

2. Second angle:
\[
x + 20 = 40 + 20 = 60^\circ
\]

3. Third angle:
\[
x + 30 = 40 + 30 = 70^\circ
\]

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

The smallest angle is:

\[
\boxed{50^\circ}
\]