Question 724520
{{{drawing(400,400,-1.5,1.5,-1.5,1.5,
locate(0,0,O),
line(cos(pi/5),sin(pi/5),cos(2pi/5),sin(2pi/5)),

line(cos(2pi/5),sin(2pi/5),cos(3pi/5),sin(3pi/5)),

line(cos(3pi/5),sin(3pi/5),cos(4pi/5),sin(4pi/5)),
blue(circle(0,0,1)),
locate(cos(3pi/5)-.1,sin(3pi/5)+.1,A),

red(line(0,0,cos(3pi/5),sin(3pi/5)),
line(0,0,cos(2pi/5),sin(2pi/5)),
line(0,0,cos(pi/5),sin(pi/5)),
line(0,0,1,0)



),

line(cos(4pi/5),sin(4pi/5),cos(5pi/5),sin(5pi/5)),

line(cos(5pi/5),sin(5pi/5),cos(6pi/5),sin(6pi/5)),

line(cos(6pi/5),sin(6pi/5),cos(7pi/5),sin(7pi/5)),

locate(cos(6pi/5)-.1,sin(6pi/5)+.1,D),

green(line(cos(3pi/5),sin(3pi/5),cos(6pi/5),sin(6pi/5))), 

line(cos(7pi/5),sin(7pi/5),cos(8pi/5),sin(8pi/5)),

line(cos(8pi/5),sin(8pi/5),cos(9pi/5),sin(9pi/5)),

line(cos(9pi/5),sin(9pi/5),cos(10pi/5),sin(10pi/5)),

line(cos(10pi/5),sin(10pi/5),cos(11pi/5),sin(11pi/5)),

locate(cos(10pi/5),sin(10pi/5)+.1,H),

green(line(cos(6pi/5),sin(6pi/5),cos(10pi/5),sin(10pi/5)))

)}}}
<pre>
Central angle AOH is made up of the 3 red central angles.
Each of those three central angles measures 360°÷10 or 36°.

So the 3 of them have measure 3×36° or 108°, so angle AOH
has measure 108°.  Therefore minor arc AH which angle ADH 
subtends has measure 108°.  

Angle ADH is an inscribed angle and an inscribed angle gas 
the measure of one-half of the measure of its subtended arc.
Angle ADH subtends the same arc which central angle AOH 
subtends. Thus the measure of angle ADH is one-half of 108° 
and is therefore 54°. 

Edwin</pre>