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2 answers:
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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 = (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°