Question

if measure angle MPL=63 HOW COULD I FIND THE OTHERS?​

Answer 1

answer:

JK = 27

NJ = 153

JL = 117

KNM = N/A

MJL = N/A

JLK = N/A

step-by-step explanation:

• you can see there are pairs of vertical angles which means they would be equal
• remember a circle adds up to 360
• the arc's measure and the angle's measure would be equal
• since we know ∠MPL is 63°, and ∠KPL is 90°, we can find the others too

∠NPM + ∠MPL = 90

∠NPM + 63 = 90

∠NPM = 27°

so, ∠JPK = 27° (since they are vertical angles)

• now, add up all the ones you know to find the other angle

63 + 90 + 27 + 27 + X = 360

• let x be the missing angle

63 + 90 + 27 + 27 + X = 360

207 + X = 360

X = 153

so, ∠JPN = 153°

• now put the measures of the arcs

ARCS:

JK = 27

NJ = 153

JL = 117

KNM = N/A

MJL = N/A

JLK = N/A

- sorry this is the furthest i can help, i have only learnt up to that so do not know how to find the rest.

Answer 2

using the relationship between intercepted arc and central angle, the missing measures are:

a. m(JK) = 27°

b. m(NJ) = 153°

c. m(JL) = 117°

d. m(KNM) = 207°

e. m(MJL) = 297°

f. m(JLK) = 333°

Central Angle and measure of Intercepted Arc

• The central angle is always equal to the measure of the intercepted arc.
• A full circle = 360 degrees.
• Half circle = 180 degrees.

Given:

m∠MPL = 63°

a. m(JK) = 180 - 90 - 63 = 27°

m(JK) = 27°

b. m(NJ) = 180 - m(JK)

m(NJ) = 180 - 27

m(NJ) = 153°

c. m(JL) = 90 + 27

m(JL) = 117°

d. m(KNM) = 180 + 27

m(KNM) = 207°

e. m(MJL) = 27 + 180 + 90 = 297°

f. m(JLK) = 360 - 27

m(JLK) = 333°

Therefore, using the relationship between intercepted arc and central angle, the missing measures are:

a. m(JK) = 27°

b. m(NJ) = 153°

c. m(JL) = 117°

d. m(KNM) = 207°

e. m(MJL) = 297°

f. m(JLK) = 333°

Learn more about central angles and intercepted arcs on:

https://brainly.com/question/2278895