The angles of a triangle measure 2x

Question

, 3x
, and 4x
. Using the Triangle Angle Sum Theorem, find the measure of the smallest angle in this triangle.(1 point)
°

Answer 1

According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is 180 degrees.

Given the angles are \( 2x \), \( 3x \), and \( 4x \), we can set up the following equation:

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

Combining like terms:

\[ 9x = 180 \]

Now, solve for \( x \):

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

Now we can find the measure of each angle:

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

Among \( 40^\circ \), \( 60^\circ \), and \( 80^\circ \), the smallest angle is:

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

Answer 2

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