Question 1209450
<br>
The response from the other "tutor" shows another faulty AI solution....<br>
Triangle ABC is isosceles with AB = AC, so angles ABC and ACB are congruent.<br>
Let 2x = measure of angle A
Then 90-x = measures of angles ABC and ACB<br>
Triangle ACD is isosceles with angles CAD and ACD congruent, so the measure of angle ACD is 2x.  Then, since the measure of angle ACB is 90-x, the measure of angle BCD is 90-3x.<br>
Triangle BCD is isosceles with CB = CD; since the measure of angle CBD is 90-x, the measure of angle CDB is also 90-x.<br>
Then the measures of the three angles in triangle BCD are 90-x, 90-x, and 90-3x.  The sum of those measures is 180 degrees:<br>
(90-x)+(90-x)+(90-3x) = 180
270-5x = 180
5x = 90
x = 18<br>
The measure of angle A is 2x = 36 degrees.<br>
ANSWER: 36 degrees<br>
An experienced problem solver might recognize the given information as describing what happens in the interior of a regular 5-pointed star, in which the measure of each of the angles at the points of the star is 36 degrees.<br>