The two green lines are parallel. The two red segments are equal and the two purple segments are equal too. The blue angle is 90°.
How big is the black angle:
+128407 Let the legs of the isosceles right triangle = 1
Then the purple segmemt on the base = sqrt (2)
The area of the right triangle = 1/2 (1)^2 = 1/2
And 1/2 = (1/2) base (height
base * height = 1
sqrt (2) height =1
height =1/sqrt (2)
So the height of this triangle will be 1/ sqrt (2)
And the perpendicular distance from the point where the purple segment meets the green line at the top left to the base = the height of the triangle = 1/sqrt (2)
So
Let A be the angle unshaded part of the 45° base angle
sin A = 1/sqrt (2) / sqrt (2) = 1/2
A = 30°
So....the shaded angle = 45 - 30 = 15°
