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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Answer from: 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

Answer from: 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°

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

Step 1: 6x-10=1; step 2: 6x=11