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Points L and M lie on a circle centered at O, and the measure of arc LM on this circle is 72 degrees.  The circle passing through points O, L, and M is drawn.  Find the measure of arc LPM on the larger circle, in degrees.

 

 
 Jun 7, 2021
 #1
avatar+69 
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arc LPM   on the larger circle =   360  -  72  =   288°

 

arc LOM on the smaller circle   =  360 -  2 (72)   =  360 - 144   =  216°

 
 Jun 7, 2021
 #2
avatar+113569 
+1

Hint:

The angle at the centre of a circle will be twice the angle at the circumference if both are standing on the same arc.

 

The arc both these angles is on is LM 

 
 Jun 7, 2021

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