Pg 522 (454) - Q25
The triangle is an isosceles triangle with AB = BC, so angle z is
equal to angle C, and since CD bisects angle C, the 2 angles that make
up angle C are each ½z degrees. Now, since you know that triangle
ADC is made up of angles x, z, and ½z, you can
write the equation x + z + ½z = 180. Also, since you
also know that angle ABC is made up of angles y, z, an z, you can write
the equation y + 2z = 180. So now you have the 2
equations:
x + z + ½z = 180, x + (3/2)z = 180, x =
180 – (3/2)z
and y + 2z = 180
Since y = (1/3)x, (1/3)x + 2z = 180.
Now substitute 180 – (3/2)z for x in the 2nd equation to get
(1/3)[180 – (3/2)z] + 2z = 180 and then solve for z:
60 – 1/2 z + 2z = 180
(3/2)z = 120
z = 80, which is E