1) m∠1 = 360°/8 = 45° . . . . . a regular octagon is 8-way rotationally symmetrical, so each sector is 1/8 of a circle.
2) m∠2 = (180° -45°)/2 = 67.5° . . . . . . the angles of a triangle add to 180°. The base angles of an isosceles triangle are equal.