## What is the measure of arc KL? 20° 40° 48° 96°

Question

What is the measure of arc KL?

20°
40°
48°
96°

in progress 0
6 days 2021-10-07T15:08:07+00:00 2 Answers 0

40

Step-by-step explanation:40

2. 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 angle
• The 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°