Problem
OA and OB are both radii, so OA = OB and triangle OAB is isosceles. Its base angles are equal, so angle OAB = angle OBA = 15 degrees.
Two radii are equal, so the triangle they form is isosceles with equal base angles.
4.G.A.2Identify SubproblemsIn triangle OAB the two base angles are equal, so angle OAB equals angle OBA (both 15 degrees).
Triangle OAB stands on two sides of the same length, OA and OB, so it is symmetric across the straight line from O that splits the angle at O in half.
Folding the triangle along that line lays the equal sides OA and OB exactly onto each other, so corner A comes to rest exactly on corner B.
With corner A resting on corner B, the base angle at A is laid directly on top of the base angle at B, and folding never changes an angle, so the two base angles are equal.
Sides OA and OB have the same length because both are radii of the same circle, each drawn from the center O out to a point on that circle.
OB and OC are radii, so OB = OC and triangle OBC is isosceles. Its base angles are equal, so angle OCB = angle OBC = 30 degrees.
The same equal-radius idea makes the second triangle isosceles too.
4.G.A.2Identify SubproblemsOA and OC are radii, so OA = OC and triangle OAC is isosceles. Its base angles are equal, so angle OCA = angle OAC = a.
The third pair of radii forms one more isosceles triangle with two equal angles, each called a.
4.G.A.2Identify SubproblemsTriangle ABC: angle B = 45°, angle A = 15+a, angle C = 30+a; summing to 180° gives 90 + 2a = 180, so a = 45 degrees.
Writing each big-triangle angle as a known part plus a, then using the 180-degree total, pins down a.
4.MD.C.7Convert To AlgebraThis only needs Grade 4 angle-adding plus knowing two equal radii make an isosceles triangle!