What is the measure of arc KL?

20°
40°
48°
96°

The question is incomplete. The complete question is here

Angle KJL measures (7x - 8)° and angle KML measures (3x + 8)°. What is the measure of arc KL, if M and J lie on the circle ?

The measure of arc KL is 40° ⇒ 2nd answer

Step-by-step explanation:

In any circle:

In a Circle

∵ M lies on the circle

∵ KL is an arc in the circle

∴ MK and ML are chords in the circle

∴ ∠KML is an inscribed angle subtended by arc KL

∵ J lies on the circle

∵ KL is an arc in the circle

∴ JK and JL are chords in the circle

∴ ∠KJL is an inscribed angle subtended by arc KL

∵ Inscribed angle subtended by the same arc are equal

∴ m∠KML = m∠KJL

∵ m∠KML = (3x + 8)°

∵ m∠KJL = (7x - 8)°

- Equate them to find x

∴ 7x - 8 = 3x + 8

- Subtract 3x from both sides

∴ 4x - 8 = 8

- Add 8 to both sides

∴ 4x = 16

- Divide both sides by 4

∴ x = 4

- Substitute the value of x in the m∠KML OR KJL to find its measure

∵ m∠KML = 3(4) + 8 = 12 + 8

∴ m∠KML = 20°

∴ m∠KJL = 20°

∵ The measure of an inscribed angle is equal to half the measure

   of its subtended arc

∴ m∠KML = (m of arc KL)

∵ m∠KML = 20°

∴ 20 = (m of arc KL)

- Multiply both sides by 2

∴ 40° = m of arc KL

The measure of arc KL is 40°

4

step-by-step explanation:

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