Question 413604
Two chords intersect in a circle forming right angles.  What is the sum of the
measures of a pair of opposite arcs?
<pre><font face = "consolas" color = "indigo" size = 4><b>
The measure of an angle formed by two intersecting chords is one-half
the sum of the measures of the arcs intercepted by it and its vertical
angles.

{{{drawing(400,400,-11,11,-11,11,
red(arc(0,0,20,-20,28.57005981,151.4299402)),
red(locate(-.3,-2,"90°")), green(locate(1.4,-3.5,"90°")),
red(arc(0,0,20,-20,241.4299402,298.5700598)),
green(arc(0,0,20,-20,151.4299402,241.4299402)),

green(arc(0,0,20,-20,298.5700598,360)),

green(arc(0,0,20,-20,360,28.57005981)),


 line(8.782329983,4.762329983,-4.76232998,-8.782329983),

line(-8.782329983,4.762329983,4.76232998,-8.782329983)

)}}}

The sum of the measures of the two red arcs is therefore twice 
the measure of the right angle indicated in red or 180° and the 
sum of the measures of the two green arcs is twice the measure of
the right angle indicated in green, or 180°.

The answer is 180°.  Were you asked to prove that, or just 
answer it?

Edwin</pre>