In the figure shown AC bar CE bar BD bar BE bar and AE bar

In the figure shown, AC bar =CE bar, = BD bar = BE bar and AE bar = DE bar If angle AED = 105 degree. find the measures of angle AEC and angle CAB.

Solution

Triangle ADE

AE = DE

So angle EAD = Angle EDA

Angle AED = 105 given

So angle EAD = angle EDA = 37.5 degree

.

Now triangle BDE

BD = BE

So angle BED = BDE = 37.5

So DEB = ABC = 105 degree

And ABE = 75 degree

So AEC = 105 - 37.5 = 67.5 degree

And CAB = 37.5 degree