Question

Q10. In the given figure, find angleBAC.
A
80 120
c С​

Answer 1

Answer:

Let the given triangle be ABC such that ∠ABC=36. A line through C meets AB at D.

Now, In △DBC,

DB=DC (Given)

hence, ∠DBC=∠DCB=36

∘

(Isosceles triangle property)

Sum of angles of triangle = 180

∠DBC+∠DCB+∠CDB=180

36+36+∠CDB=180

∠CDB=108

Now, ∠ADC=180−∠ADB

∠ADC=180−108

∠ADC=72

∘

in △ADC,

∠ADC=∠DAC=72

∘

(Isosceles triangle property, AC= CD is given)

Sum of angles = 180

∠ADC+∠CAD+∠ACD=180

72+72+x=180

x=180−144

x=36°

thank you