Reasoning · Grade 4-1 Polygons and Angles
Problem
The crease is a mirror, so both sides match.
A fold is a reflection, and a reflection never changes an angle's size — so the crease always bisects the angle between an edge and where that edge lands.
8.G.A.1Create A Physical RepresentationOne angle of the new triangle is 70 degrees.
The angle we want lives at Q, so the useful move is to find a triangle that has Q as a corner and reaches back to the one place where a measure is known.
4.G.A.1Draw A DiagramBy the mirror the opposite angle is also 70 degrees.
When one straight line crosses two parallel lines, the angles it makes with them repeat, so a measure known at the top edge is automatically known at the bottom edge — no new measuring needed.
8.G.A.5Identify SubproblemsThe 70 degrees known at the top edge is automatically known at the bottom edge, because the crease crosses two parallel lines.
One straight line crossing two parallel lines repeats the same angles at both crossings.
The crease is a mirror line, so the angle between an edge and the crease is copied exactly on the other side of it.
The last corner is 180 − 140 = 40 degrees.
Two equal base angles of 70° leave only 40° for the third corner — the same 180° budget every triangle has to share out.
8.G.A.5Identify SubproblemsAngle 1 equals it, so 40 degrees.
Two straight lines crossing make an X, and the two angles facing each other across the X are always the same size.
7.G.B.5Identify SubproblemsA fold is a mirror, so the crease always splits the angle between an edge and where that edge lands into two equal halves.