February 21st, 2016, 01:30 PM  #1 
Newbie Joined: Feb 2016 From: Saudi Arabia Posts: 2 Thanks: 0  Need help in math circle theorems
please see the picture find the labelled angles asap Last edited by amni1234; February 21st, 2016 at 01:45 PM. 
February 21st, 2016, 02:03 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,755 Thanks: 1405 
hints ... 1. sketch in the radius from the center O to the vertex of angle $a$ 2. if O is the center, the 38 degrees is one of two base angles of an isosceles triangle 
February 23rd, 2016, 01:00 AM  #3 
Newbie Joined: Feb 2016 From: israel Posts: 17 Thanks: 3 
Sorry for my bad french... a triangle inside a circle has some special features. The center of the circle is the point where all the triangle's bisections meet. One more hint: there is a known relation between a central angle and a circumferential angle inside a circle. Last edited by skipjack; February 23rd, 2016 at 01:07 AM. 
February 23rd, 2016, 04:42 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,198 Thanks: 872 
Two geometric theorems are needed here: The measure of an angle with vertex at the center of a circle is equal to the angle measure of the arc it subtends. The measure of an angle with vertex on the circumference of a circle is equal to half the angle measure of the arc it subtends. Since angles a and b subtend the same arc, we must have measure of angle a equal to half the measure of angle b. Using "A" and "B" to denote those measures, in degrees, B= 2A. Further, with the angle at the center of measure B, the "reflex angle", interior to the quadrilateral, is 360 B. Finally, the interior angles in any quadrilateral add to 360 degrees so we must have 18+ 360 B+ 24+ A= 18+ 360 2A+ 24+ A= 402 A= 360 so A= 402 360= 42 degrees and B= 2(42)= 84 degrees. 

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circle, math, theorems 
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