Question 1191608

The measure of the angke formed by two tangents to a circle is 80 degrees. Find the measure of the intercepted arc. Show your solution 
<pre>Let the intercepted/smaller arc be A
Then larger arc = 360  -  A
As the measure of the angle formed by 2 tangents to a circle is {{{1/2}}} the difference between the 2 arcs, we get: {{{matrix(2,3, (1/2)(360  -  A  -  A), "=", 80, (1/2)(360  -  2A), "=", 80)}}}
                             360 - 2A = 160 ----- Cross-multiplying
                                 - 2A = 160 - 360
                                 - 2A = - 200
<font color = red><font size = 4><b>Intercepted/smaller arc, or {{{highlight_green(matrix(1,3, A, "=", (- 200)/(- 2))))}}} = 100<sup>o</sup></font></font></b></pre>