Find unknown angles in any triangles - Reasoning

In the given problem, students are tasked with finding the unknown angles in a triangle using their knowledge of geometry and the properties of shapes. The key information provided is that the sum of angles 'a', 'b', and 'c', along with an additional 65 degrees, equals 180 degrees. This is based on the principle that the sum of the angles in any triangle is always 180 degrees. To solve for the unknown angles, the students must apply this principle and use reasoning skills to deduce the values of each angle.

The solution to the problem reveals that angles 'a' and 'b' are equal, and angles 'e' and 'd' are both 90 degrees, indicating that they are right angles. This suggests that the triangle in question is an isosceles triangle, where two sides and their corresponding angles are equal. Given that angle 'c' is 65 degrees, the remaining two angles, 'a' and 'b', can be found by setting up the equation a + b + 65 degrees + 65 degrees = 180 degrees. By subtracting the known angles from 180 degrees and dividing the result by two, we find that angles 'a' and 'b' are both 25 degrees. The problem encourages students to show their work and follow logical steps to arrive at the correct values for each angle.