Problem
The 5 angles 1, 2, 3, 4, 5 each stand alone. The problem tells us all 5 are acute, so all 5 single angles count.
An angle is the opening between two rays; each gap between neighboring rays is one such angle.
4.MD.C.5Make A Systematic ListJoining two neighbors gives (1+2), (2+3), (3+4), (4+5): 4 larger angles, each about 72 degrees, so all 4 are still acute.
Angle measure adds: two angles laid side by side make one angle whose size is their sum.
4.MD.C.7Make A Systematic ListAn angle formed by joining two neighboring small angles is itself acute, so each pair of neighbors adds another acute angle to the count.
Joining two neighboring small angles makes one larger angle whose measure is exactly those two small angles added together.
The two small angles sit right next to each other with no gap and no overlap, so together they fill the one larger opening completely.
Two of the small angles added together still come to less than a right angle, because all five of them must share one straight angle between them.
The five small angles lie side by side along the straight base line, so all five together measure exactly 180 degrees and each one takes only a small part of it.
Combining three or more (about 108 degrees) passes a right angle, so those 3 + 2 + 1 = 6 longer angles are not acute.
Keep adding pieces of the 180-degree half-turn and the angle eventually reaches a right angle and beyond, so it stops being acute.
4.MD.C.7Identify SubproblemsAcute angles are the 5 singles plus the 4 pairs.
Just total up the groups we kept.
4.MD.C.7Make A Systematic ListList the angles by how many pieces they use, then keep only the ones still smaller than a right angle - that is Grade 4 angle sense you already have!