Question

se the image to answer the question.

A triangle is shown with its angles measuring 2 x, 96 degrees, and x plus 12 degrees.

Find the measure of the smallest angle of the triangle.(1 point)
°

Answer 1

To find the measure of the smallest angle of the triangle, we need to first set up an equation using the property that the sum of the angles in a triangle equals 180 degrees.

The angles of the triangle are given as:
- \( 2x \)
- \( 96^\circ \)
- \( x + 12^\circ \)

Setting up the equation:

\[
2x + 96 + (x + 12) = 180
\]

Simplifying the equation:

\[
2x + 96 + x + 12 = 180
\]

Combine like terms:

\[
3x + 108 = 180
\]

Next, subtract 108 from both sides:

\[
3x = 72
\]

Now, divide both sides by 3 to solve for \( x \):

\[
x = 24
\]

Now we can find the measures of the angles:

1. \( 2x = 2(24) = 48^\circ \)
2. \( 96^\circ \) (given)
3. \( x + 12 = 24 + 12 = 36^\circ \)

The measures of the angles are:
- \( 48^\circ \)
- \( 96^\circ \)
- \( 36^\circ \)

To find the smallest angle, we compare the measures:

- \( 48^\circ \)
- \( 96^\circ \)
- \( 36^\circ \)

The smallest angle is \( 36^\circ \).

Therefore, the measure of the smallest angle of the triangle is:

\[
\boxed{36}
\]