<PRE><B>Question 1173327</B>
&lt;br&gt;
(1) The sum of the measures of all the arcs of the circle is 360.&lt;br&gt;
(2) The measure of any arc is twice the measure of the inscribed angle that cuts off that arc.&lt;br&gt;
(3) The sum of the measures of the angles of a triangle is 180. (Note that this follows from (1) and (2), using triangle BXY....)&lt;br&gt;
Given:
(a) angle BXY = 40
(b) angle YBX = 55
(c) arc BA = 70&lt;br&gt;
To find:&lt;br&gt;
arc AB: given&lt;br&gt;
arc BX: cut off by angle BYX, whose measure can be determined from (3)&lt;br&gt;
arc YZ (I will assume that is supposed to be YX): cut off by given angle YBX; use (2)&lt;br&gt;
arc AY: Use (1); you know the measures of all the other arcs&lt;br&gt;
arc ABX: sum of the measures of arcs AB and BX&lt;br&gt;
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