I’ve a question about this. Its mostly about supplementary angles. Lets say the top left angle is 1, bottom left angle is angle 2, bottom right angle is 3 and bottom top right angle is angle 4.
Ok so now we are given the angle 4 which is 135. We can use this to calculate angle 3: 180-135=45
My confusion is why can’t we use the same 180 rule to find angle 2. So 180-45=135 for angle 2. I know that’s not correct. I want to know why is the 180 rule only used for angle 3 and 4 and not 2 and 3.
I did a lot of back and forth with GPT. From that debate, i came to the conclusion that the key to this supplementary rule is parallel lines. For example, the angles 3 and 4 on the two ends of the line add up to 180 because the slanted lines cuts two parallel lines while the bottom line doesn’t hence angle 2 and 3 are NOT equal to 180.
The figure is an isosceles trapezoid and angle 1 = angle 4 while Angle 2 = Angle 3.
Like you said yourself, parallelism is the key, coupled with the fact that the slanted legs are both 10, it follows that the angles are correspondingly equal.
