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

Answers ( )

    0
    2021-10-07T15:09:28+00:00

    Answer:

    40

    Step-by-step explanation:40

    0
    2021-10-07T15:10:03+00:00

    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 ?

    Answer:

    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 = \frac{1}{2} (m of arc KL)

    ∵ m∠KML = 20°

    ∴ 20 = \frac{1}{2} (m of arc KL)

    – Multiply both sides by 2

    ∴ 40° = m of arc KL

    The measure of arc KL is 40°

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