Problem
The fold makes two equal angles at N
The fold is a mirror, so the 25 deg slant at N is copied to another 25 deg on the crease's far side.
A fold is a mirror: whatever angle the paper makes on one side of the crease, it makes the same angle on the other side.
4.G.A.1Create A Physical RepresentationUse the straight bottom edge
The bottom edge at N is a straight 180 deg, and the two 25 deg base slants plus the peak angle a fill that straight line.
The folded flap is an isosceles triangle with two equal base angles of 25 deg, so the top angle is the rest of the 180 deg triangle total.
4.MD.C.7Identify SubproblemsThe peak angle a equals 180 degrees minus the folded flap's two equal base angles.
Why?
The standing flap and the bottom edge close up into a triangle, and a triangle's three angles always fill 180 degrees, so the peak is whatever is left after the other two.
Why?
The other two angles are the flap's two base angles; they are equal to each other, and one of them is the 25 degree slant already marked at N, so both are the same size.
Why?
The fold lays the paper onto itself like a mirror across the crease, copying the slant angle on one side of the crease exactly onto the other side.
Compute the peak angle
Subtract the two equal base angles from 180 deg.
Two small 25 deg corners leave a wide 130 deg angle at the top of the thin folded flap.
4.MD.C.7Identify SubproblemsA fold is a mirror, so the two base angles match at 25 deg each; the peak is just 180 deg minus those two!
- The fold makes two equal angles at N
- Use the straight bottom edge
- Compute the peak angle