Answer:
We have two angles measuring 115° and 75°. Let's call the other two angles "x" and "y." According to the problem, their ratio is 2:15.
So, we can set up an equation:
x/y = 2/15
Now, we know that the sum of the angles in a quadrilateral is 360 degrees. Therefore:
115 + 75 + x + y = 360
Simplify the equation:
190 + x + y = 360
Now, let's solve for x and y:
x + y = 360 - 190
x + y = 170
We also have the ratio:
x/y = 2/15
We can use this ratio to express one of the variables in terms of the other:
x = (2/15) * y
Now, substitute this into the equation x + y = 170:
(2/15) * y + y = 170
Multiply both sides by 15 to eliminate the fraction:
2y + 15y = 170 * 15
Combine like terms:
17y = 2550
Now, divide by 17 to find y:
y = 2550 / 17
y ≈ 150
Now that we know the value of y, we can find x using the ratio:
x = (2/15) * y
x = (2/15) * 150
x = 20
So, the correct measures of the two angles are x = 20 degrees and y = 150 degrees.