Mathematics, 07.04.2020 19:27, babbity2009

Answer in the 10-1 quiz intro to circles, central angles, arcs, and chord

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answered: haley4023

The measures of the angles are:

Arc JK is 27 degrees.Arc NJ is 153 degrees.Arc JL is 117 degrees.Angle KNM is 207 degrees.Angle MJL is 297 degrees.Angle JLK is 333 degrees.

From the attached image, we have:

The center of the circle is P.The diameters are lines JM and NK.

The above highlights mean that:

$\mathbf{\angle NPM \cong \angle JPK}$

$\mathbf{\angle NPL = 90}$

So, we have:

$\mathbf{\angle NPM +\angle MPL = 90}$

Substitute 63 for MPL

$\mathbf{\angle NPM +63 = 90}$

Subtract 63 from both sides

$\mathbf{\angle NPM = 27}$

$\mathbf{\angle NPM \cong \angle JPK}$ means that

$\mathbf{\angle JPK = 27}$

So, arc JK is 27 degrees

Arc NJ is calculated using:

$\mathbf{NJ = 180 - JK}$ --- measure of angle in a semicircle

So, we have:

$\mathbf{NJ = 180 - 27}$

$\mathbf{NJ = 153}$

Arc JL is calculated using:

$\mathbf{JL = 90+ JK}$

So, we have:

$\mathbf{JL = 90 + 27}$

$\mathbf{JL = 117}$

The measure of angle KNM is calculated using:

$\mathbf{\angle KNM = 180 + \angle NPM}$

So, we have:

$\mathbf{\angle KNM = 180 + 27}$

$\mathbf{\angle KNM = 207}$

The measure of angle MJL is calculated using:

$\mathbf{\angle MJL = 180 + JK + 90}$

So, we have:

$\mathbf{\angle MJL = 180 + 27 + 90}$

$\mathbf{\angle MJL = 297}$

Lastly, the measure of angle JLK is calculated using:

$\mathbf{\angle JLK = 180 + \angle MPL + 90}$

So, we have:

$\mathbf{\angle JLK = 180 + 63 + 90}$

$\mathbf{\angle JLK = 333}$

Read more about circles, central angles, arcs, and chord at:

link

answered: SoccerHalo

a. 27

b. 153

c. 117

d. 207

e. 297

f.333

Step-by-step explanation:

In the circle, the center point is P, JM and NK are two diameters of the circle

=> JM intersects NK at point P

=> ∠MPN = ∠JPK

As P is on line segment NK

=> ∠MPN + ∠MPL + ∠LPK = 180°

Given that: ∠MPL = 63°; ∠LPK = 90°

=> ∠MPN + 63° + 90° = 180°

=> ∠MPN = 180° - 90° - 63° = 27°

=> ∠MPN = ∠JPK = 27°

As P is on line segment MK=J

=> ∠MPN + ∠NPJ = 180°

=> 27 + ∠NPJ = 180

=> m∠NPJ = 180 - 27 = 153°

As P is the center point of the circle and J, K, L, M, N are points on the circle, so that we have:

+) m arc JK = m∠JPK = 27°

+) m arc NJ = m∠NPJ = 153°

+) m arc JL = m∠JPL = m∠JPK + m∠KPL = 27 + 90 = 117°

+) m arc KNM = m arc KN + m arc NM = 180° + ∠MPN = 180 + 27 = 207°

+) m arc MJL = 360° - m arc ML = 360° - ∠MPL = 360 - 63 = 297°

+) m arc JLK = 360° - m arc JK = 360 - 27 = 333°

answered: Guest

step-by-step explanation:

answered: Guest

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x