A trigangular region of a community college parking lot was measured. The measure of the first angle of this triangle is doubled the measure of the second angle. The measure of the third angle is 89 degree greater than double the measure of the first angle. what is the measurement of all three
A1=2A2
A3=89+2A1
A1+A2+A3=180
does that help?
To solve this problem, we can let the measure of the second angle be represented by the variable "x".
According to the given information, the measure of the first angle is double the measure of the second angle. So, the measure of the first angle would be 2x.
The measure of the third angle is 89 degrees greater than double the measure of the first angle. Therefore, the measure of the third angle would be 2(2x) + 89.
To find the measurement of all three angles, we need to add up the measures of the angles in a triangle. The sum of the interior angles in a triangle is always 180 degrees.
So, we can set up an equation based on this information:
x + 2x + (2(2x) + 89) = 180
Simplifying the equation:
x + 2x + 4x + 89 = 180
7x + 89 = 180
7x = 180 - 89
7x = 91
x = 91/7
x ≈ 13
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their measurements:
First angle: 2x = 2 * 13 = 26
Second angle: x = 13
Third angle: 2(2x) + 89 = 2(2*13) + 89 = 52 + 89 = 141
Therefore, the measurements of the three angles are approximately: 26 degrees, 13 degrees, and 141 degrees.