Question

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 = °

Answer 1

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).

$Arc(IK)\cong Arc(JK)$

$mArc(IK)=mArc(JK)$

Substitute the given values.

$11x+2=12x-7$

Isolate variable terms on one side.

$7+2=12x-11x$

$9=x$

The measure of Arc(IK) is

$mArc(IK)=11(9)+2=101^{\circ}$

The measure of Arc(IJK) is

$mArc(IJK)=360-mArc(IK)=360-101=259^{\circ}$

Therefore, the measure of Arc(IJK) is 259°.

Answer 2

Answer:

202

Step-by-step explanation: