Answer:
see explanation
Step-by-step explanation:
The 3 arcs AB, BC and CA form the circle and equal 360°, thus
2x + 3x + 4x = 360
9x = 360 ( divide both sides by 9 )
x = 40
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The inscribed ∠ 1 is half the measure of its intercepted arc, that is
∠ 1 = 0.5 × arc BC = 0.5 × 3x = 0.5 × 120° = 60°
The inscribed ∠ 2 is also half its intercepted arc
∠ 2 = 0.5 × BC = 0.5 × 120° = 60°
The angle at the centre ∠ 3 is twice the angle at the circumference ∠ 1
∠ 3 = 2 × ∠ 1 = 2 × 60° = 120°
The triangle OBC is isosceles ( OB = OC, the radii of the circle )
Thus the base angles are congruent, thus
∠ 4 = [tex]\frac{180-120}{2}[/tex] = [tex]\frac{60}{2}[/tex] = 30°
