The angles of a triangle measure 2x , 3x , and 4x . Using the Triangle Angle Sum Theorem, find the measure of the smallest angle in this triangle

Answer 1

To find the angles of the triangle given as \(2x\), \(3x\), and \(4x\), we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is equal to \(180^\circ\).

Setting up the equation:

\[ 2x + 3x + 4x = 180^\circ \]

Combining like terms:

\[ 9x = 180^\circ \]

Now, solve for \(x\):

\[ x = \frac{180^\circ}{9} = 20^\circ \]

Now we can find the measures of each angle:

• The first angle: \(2x = 2(20^\circ) = 40^\circ\)
• The second angle: \(3x = 3(20^\circ) = 60^\circ\)
• The third angle: \(4x = 4(20^\circ) = 80^\circ\)

The angles of the triangle are \(40^\circ\), \(60^\circ\), and \(80^\circ\).

The smallest angle in this triangle is:

\[ \boxed{40^\circ} \]