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

The measures of the angles are:

From the attached image, we have:

The above highlights mean that:

So, we have:

Substitute 63 for MPL

Subtract 63 from both sides

means that

So, arc JK is 27 degrees

Arc NJ is calculated using:

--- measure of angle in a semicircle

So, we have:

Arc JL is calculated using:

So, we have:

The measure of angle KNM is calculated using:

So, we have:

The measure of angle MJL is calculated using:

So, we have:

Lastly, the measure of angle JLK is calculated using:

So, we have:

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

link

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°

303.14159265

Step-by-step explanation:

3.14+300= 303.14