Answer: Let's denote the two unknown angles as x and y.
We know that the sum of the angles in any quadrilateral is 360°, so we can set up an equation using this fact:
235° + 40° + x + y = 360°
Simplifying this equation, we get:
x + y = 85° (equation 1)
We also know that the other two angles are in a ratio of 5:12. This means that:
x/y = 5/12
Multiplying both sides by y, we get:
x = (5/12)y (equation 2)
Now we can substitute equation 2 into equation 1 and solve for y:
(5/12)y + y = 85°
(17/12)y = 85°
y = (12/17) * 85°
y = 60°
Substituting y = 60° into equation 2, we can solve for x:
x = (5/12) * 60°
x = 25°
Therefore, the two angles that are in a ratio of 5:12 measure 25° and 60°, respectively.
Explanation: