Find the measure of the smallest angle of the triangle

Question

The top point is 96°
Bottom left is 2X
Bottom right is X +12

Answer 1

To find the measure of the smallest angle of the triangle, we first need to determine the values of X and 2X.

We know that the sum of the interior angles of a triangle is always 180 degrees. So, we can write the following equation:

96 + 2X + (X + 12) = 180

Now, we can simplify the equation:

3X + 108 = 180
3X = 72
X = 24

Now that we have found the value of X, we can find the measures of the bottom left and bottom right angles:

Bottom left angle = 2(24) = 48 degrees
Bottom right angle = 24 + 12 = 36 degrees

To find the measure of the smallest angle, we compare the three angles:

96° (top) > 48° (bottom left) > 36° (bottom right)

Therefore, the smallest angle of the triangle is 36 degrees.