Answer:
Let x be the first unknown angle, and y be the second unknown angle.
We know that the sum of the three angles in a triangle is 180 degrees, so:
85 + 9kx + 10kx = 180
where k is a constant representing the ratio of the other two angles.
Simplifying the equation, we get:
19kx = 95
Dividing both sides by 19k, we get:
x = 5/k
Since the ratio of the other two angles is 9:10, we know that:
y = 9kx = 9k(5/k) = 45
So the measures of the two unknown angles are:
x = 5/k and y = 45
We cannot find the exact measures of x and y without more information, but we know that x and y are in a ratio of 9:10 and their sum is 180 - 85 = 95 degrees. We can set up the following equation to solve for k:
5/k + 45/k = 95
50/k = 95
k = 50/95
Using this value of k, we can find the measures of x and y:
x = 5/k = 5/(50/95) = 9.5
y = 9kx = 9(50/95)(9.5) = 47.37
Therefore, the measures of the two unknown angles are x = 9.5 degrees and y = 47.37 degrees (rounded to two decimal places).
Explanation: