Question

Match the statements with their values. Tiles when ΔABC is an isosceles triangle with when and ΔABC is an isosceles triangle with when and ΔPQR is an isosceles triangle with when and points D and E are the midpoints of and , respectively, in ΔABC Pairs 55° arrowBoth 180° arrowBoth 45° arrowBoth 30° arrowBoth

Answer 1

For an isosceles triangle angles ABC=ACB=35
Let the angle ADB be x
then ADC is 180-x
as AD is median so BD=CD
and for isosceles triangle AB=AC 
so AB/AC=BD/CD=1
By angle bisector theorem
 BAD=CAD=y  (just take it)
for an triangle BAD 35+x+y=180...(1)
for an triangle DAC 35+180-x+y=180...(2)
35+y=x
therefore  
35+34+y+y=180
2y+70=180
2y=100
y=55
therefore angle BAD=CAD=55