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:
- \( 2x = 2(24) = 48^\circ \)
- \( 96^\circ \) (given)
- \( x + 12 = 24 + 12 = 36^\circ \)
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:
\[ \boxed{36} \]
1 answer