Question

ABC IS A TRIANGLE WITH D,E,F ARE THE MIDDLE POINTS OF SIDES BC,CA,AB
RESPECTIVELY.Angle-dac=65 and angle-acb=23.Then find the value of angle-bac.

Answer 1

given that
from the above diagram
∠dac = 65
∠acb = 23
we know that
the sum of the interior angles are equal to the opposite the external angle.
than
∠bad +∠abc = ∠adc
so we think that ∠abd as 'x'.
then ∠bad = 92-x
so from Δabd
∠abc+∠bad+∠adb = 180
x+92-x+88 = 180
180 = 180
in the same way from the Δabc
x+92-x+65+23 = 180
180 = 180
so from the above
we should think that x = 23
means ∠b = ∠c
then the values are satisfied
then
from ∠bad = 92-x
                    =92-23
                    =69
then angle bac = 69+65
                          =134.