To find the measures of the missing angles, we can use the fact that the angles in a triangle add up to 180 degrees.
Given:
Angle 1 = 97 degrees
Angle 2 = 114 degrees
Let's denote the missing angles as Angle 3 and Angle 4.
Now, we can set up an equation based on the sum of angles in a triangle:
Angle 1 + Angle 2 + Angle 3 = 180 degrees
Substitute the known values:
97 degrees + 114 degrees + Angle 3 = 180 degrees
Combine the known angles:
211 degrees + Angle 3 = 180 degrees
Now, isolate Angle 3 by subtracting 211 degrees from both sides:
Angle 3 = 180 degrees - 211 degrees
Angle 3 = -31 degrees
So, Angle 3 measures -31 degrees. Since angles cannot be negative in a geometric context, it's likely that there was an error in the angle measurements or the problem statement.
If you have another angle to find (Angle 4), you can use the fact that the sum of angles in a quadrilateral is 360 degrees (assuming this is a quadrilateral). However, without more information, it's not possible to determine the value of Angle 4.