A trangular region of a community college parking lot was measured. The measure of thefirst angle of this triangle is double the measure of the second angle. the measure of the third angleis 131 greater than double the measure of the first angle. what are the measurements of all three angles?
To find the measurements of the three angles, let's assign variables to them. Let's say the second angle is x.
According to the problem, the measure of the first angle is double the measure of the second angle, so the first angle would be 2x.
Also, the measure of the third angle is 131 greater than double the measure of the first angle. Therefore, the third angle would be 2(2x) + 131.
Now, we know that the sum of the angles of a triangle is always 180 degrees. So, we can set up the equation:
x + 2x + (2(2x) + 131) = 180
Simplifying and solving this equation will give us the value of x, which we can then use to find the measurements of all three angles.
Let's solve the equation step by step:
x + 2x + 4x + 131 = 180
7x + 131 = 180
7x = 180 - 131
7x = 49
x = 49 / 7
x = 7
Now that we have the value of x, we can substitute it back into our calculations to find the measurements of all three angles.
First angle = 2x = 2 * 7 = 14
Second angle = x = 7
Third angle = 2(2x) + 131 = 2(2 * 7) + 131 = 2(14) + 131 = 28 + 131 = 159
Therefore, the measurements of the three angles are:
First angle = 14 degrees
Second angle = 7 degrees
Third angle = 159 degrees