Question
A triangle has the angle measures 96°, 2x°, and (x+12)°. Find the measure of the smallest angle of the triangle.
Answers
GPT 3.5
To find the measure of the smallest angle, we can start by setting up an equation since the sum of the angles in a triangle is 180°.
So, let's add up the three angle measures:
96° + 2x° + (x+12)° = 180°
Simplify the equation:
96° + 2x° + x° + 12° = 180°
3x + 108 = 180
Subtract 108 from both sides:
3x = 72
x = 24
Now that we have found the value of x, we can substitute it back into the expression for the smallest angle:
2x = 2(24) = 48
Therefore, the smallest angle of the triangle is 48°.
So, let's add up the three angle measures:
96° + 2x° + (x+12)° = 180°
Simplify the equation:
96° + 2x° + x° + 12° = 180°
3x + 108 = 180
Subtract 108 from both sides:
3x = 72
x = 24
Now that we have found the value of x, we can substitute it back into the expression for the smallest angle:
2x = 2(24) = 48
Therefore, the smallest angle of the triangle is 48°.