To find the measure of each angle in the given triangle, we should remember that the sum of all angles in a triangle is always 180 degrees.
Given:
1. One angle measures 64 degrees.
2. The second angle is three times the third angle.
Let's denote the measure of the third angle as 'x' degrees. Therefore, the second angle, being three times the third angle, will be '3x' degrees.
Since the sum of all angles in a triangle is 180 degrees, we can write an equation to represent this relationship:
64 (first angle) + 3x (second angle) + x (third angle) = 180
Now, let's combine like terms by adding together the 'x' and '3x':
64 + 3x + x = 180
64 + 4x = 180
Next, we need to solve for 'x'. Start by subtracting 64 from both sides of the equation to isolate the term '4x':
4x = 180 - 64
4x = 116
Now, divide both sides by 4 to solve for 'x':
x = 116 / 4
x = 29
Therefore, the third angle measures 29 degrees.
Since the second angle is three times the third angle, we calculate it as follows:
Second angle = 3x
Second angle = 3 29
Second angle = 87 degrees
To summarize:
- The first angle is given as 64 degrees.
- The second angle is three times the third angle, which is 87 degrees (since 3 29 = 87).
- The third angle is 29 degrees.
All three angles add up to 180 degrees (64 + 87 + 29 = 180), which satisfies the condition that the sum of the angles in a triangle must equal 180 degrees.
