Question

In the figure l(AD)= l(BD)=l(AE)=l(EC) and measure angle AEB =100° and mesure angle ABE=20° then find measure of angle CAB

Answer 1

Answer:

110 degrees

(Notice that in the problem in the book, it does not say that lengths BD and AE are equal!)

Step-by-step explanation:

Since AD = BD, the triangle ABD is isosceles.  So

angle BAD = angle ABD = 20 degrees.

Next, by the external angle theorem,

angle ACE + angle CAE = angle AEB = 100 degrees.

Since sides AE and EC are equal, triangle ACE is isosceles, so

angle ACE = angle CAE.

Since these angles are equal and add up to 100 degrees, they are each 50 degrees.  In particular, angle CAE = 50 degrees.

Again using the external angle theorem,

angle ADE = angle ABD + angle BAD = 20 + 20 = 40.

Since the sum of the angles in a triangle is 180 degrees, this leads us to

angle DAE = 180 deg - angle ADE - angle AED = ( 180 - 40 - 100 ) deg = 40 degrees.

Finally,

angle CAB = angle CAE + angle DAE + angle BAD

= ( 50 + 40 + 20 ) degrees

= 110 degrees.

P.S. Notice that angle ADE = angle DAE = 40 degrees, so triangle ADE is also isosceles, so AE = EC = ED.

Answer 2

this is your answer