Concept:Angles around a point sum to 360∘, and perpendicular lines form a 90∘ angle.Explanation:Since AO⊥OB, ∠AOB=90∘.The angles 4x, 3x, 2x, and 90∘ meet at point O.Therefore, 4x+3x+2x+90∘=360∘.Simplifying gives 9x+90∘=360∘.Subtract 90∘ from both sides: 9x=270∘.Divide both sides by 9: x=30∘.Answer:x=30∘, which is Option D.
