Question

Find the measure of the smallest angle of the triangle.

The image shows a triangle. The top angle shows the number 96 degrees. The bottom left angle shows 2x. The bottom right angle shows x + 12 degrees.

Answer 1

To find the measure of the smallest angle in the triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Given the angles in the triangle, we have:

1. Top angle = 96 degrees
2. Bottom left angle = \(2x\)
3. Bottom right angle = \(x + 12\)

We can set up the equation as follows:

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

Now, simplify the equation:

\[
96 + 2x + x + 12 = 180
\]
\[
3x + 108 = 180
\]

Next, isolate \(3x\):

\[
3x = 180 - 108
\]
\[
3x = 72
\]

Now, solve for \(x\):

\[
x = \frac{72}{3} = 24
\]

Now we can find the measures of the bottom left and bottom right angles:

1. Bottom left angle (\(2x\)):
\[
2x = 2 \cdot 24 = 48 \text{ degrees}
\]

2. Bottom right angle (\(x + 12\)):
\[
x + 12 = 24 + 12 = 36 \text{ degrees}
\]

Now, we have the measures of all angles:

- Top angle = 96 degrees
- Bottom left angle = 48 degrees
- Bottom right angle = 36 degrees

Finally, the smallest angle in the triangle is:

\[
\text{Smallest angle} = 36 \text{ degrees}
\]

Therefore, the measure of the smallest angle of the triangle is \( \boxed{36} \) degrees.