In ⊙H, Arc I K ≅ Arc J K, mArc I K = (11x + 2)°, and mArc J K = (12x – 7)°. Circle H is shown. Line segments H I, H K, and H J are radii. Lines are drawn to connect points I and K, and points K and J to form congruent secants. What is the measure of Arc I J K? mArc I J K = °

Accepted Solution

Answer:259°Step-by-step explanation:Given information : In ⊙H, Arc(IK) ≅ Arc(JK), mArc(IK)=(11x+2)°, and mArc(JK)=(12x-7)°. We need to find the measure of Arc (IJK).[tex]Arc(IK)\cong Arc(JK)[/tex][tex]mArc(IK)=mArc(JK)[/tex]Substitute the given values.[tex]11x+2=12x-7[/tex]Isolate variable terms on one side.[tex]7+2=12x-11x[/tex][tex]9=x[/tex]The measure of Arc(IK) is[tex]mArc(IK)=11(9)+2=101^{\circ}[/tex]The measure of Arc(IJK) is[tex]mArc(IJK)=360-mArc(IK)=360-101=259^{\circ}[/tex]Therefore, the measure of Arc(IJK) is 259°.