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:

Inscribed angles subtended by the same arc are equal If the vertex of an angle lies on the circles and its two sides are chords in the circle, then it called inscribed angleThe measure of an inscribed angle is equal to half the measure of its subtended arc

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°

The answer is 3. parallelogram

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