Question

Line BE is congruent to line EC, measure of angle AEC =76 degrees and measure of angle EAB=41 degrees. Find measure of angle AEB.

Answer 1

We know that the interior angles of any triangle have to add 180°, we know angles AEC and angles EAC from triangle AEC, then we have that the next step is:

$m\angle ACE=63\text{ Sum of angles in triangle}$

Now, since line BE and EC are congruent this means that triangle BCE is isosceles, and then the next step would be:

$m\angle CBE=63\text{ Base angle of an isosceles triangle}$

We notice that angles CBE and ABE form a linear pair, then we have:

$m\angle ABE=117\text{ Linear pair}$

Finally, once again we use the fact that the sum of interior angles is equal to 180°, then we have:

$m\angle AEB=22\text{ Sum of angles in triangle}$