Problem
Rotating 90 degrees clockwise about A sends B to D, so ray AB turns to ray AD through exactly 90 degrees: angle BAD = 90 degrees.
The amount you turn the shape is exactly the angle between a point and its rotated image.
4.MD.C.5Visualize Spatial RelationshipsRotation does not change angle sizes, so triangle ADE is still equilateral and its angle at A, angle DAE, is 60 degrees.
Turning a shape does not stretch or bend it, so every angle stays the same size.
4.G.A.2Visualize Spatial RelationshipsThe angle at A in the rotated triangle, angle DAE, is still 60 degrees.
Angle DAE is the corner at A of triangle ADE, and triangle ADE is just triangle ABC turned around A, so that corner is the same size it was before the turn.
Before it was turned the shape was equilateral triangle ABC, and every corner of an equilateral triangle measures 60 degrees.
An equilateral triangle has three equal corners that together fill a straight angle of 180 degrees, so each corner is 180 divided by 3, which is 60 degrees.
Turning the shape around A only spins it in place without stretching or bending it, so a corner that measured 60 degrees still measures 60 degrees after the turn.
Ray AE sits inside the 90° turn, with angle DAE = 60° taking up part of it: angle 1 = 90 - 60 = 30 degrees.
Angle measure is additive, so the leftover piece of the 90-degree turn after the 60-degree angle is the answer.
4.MD.C.7Identify SubproblemsThis only needs Grade 4 angle-subtracting plus knowing a turn keeps every angle the same size!