<PRE><B>Question 47501</B>
Parallelogram ABCD has diagonal AC equal in length to side AB. CD is produced to E so that D is between E and C. If angle BAC = 30 degrees, find the size of angle ADE
Please show any working out
Thanks
IN TRIANGLE ABC
AB=AC...GIVEN
SO ANGLE ACB=ANGLE ABC=X SAY
ANGLE CAB=30...GIVEN
HENCE X+X+30=180
2X=180-30=150
X=75=ANGLE ABC
SINCE ABCD IS A PARALLELOGRAM
ANGLE ABC = ANGLE ADC......OPPOSITE ANGLES.
HENCE ANGLE ADC = 75
SO ANGLE ADE = 180-ANGLE ADC=180-75=105...SINCE CDE IS A STAIGHT LINE AND DA IS STANDING ON IT FORMING  ADJACENT ANGLES ADE AND ADC WHICH ARE SUPPLEMENTARY </PRE>