In ΔABC, D is a point on the side BC such that AB = AD = DC. If ∠BAD = 28°, find ∠BAC.

Question

In ΔABC, D is a point on the side BC such that AB = AD = DC
If ∠BAD = 28°, find ∠BAC

Ankita Agarwal · Accepted Answer

Dear Student,

In △ABDLet ∠ABD=∠ADB =x   AB=ADand∠BAD+∠ABD+∠ADB=180°        Sum of all the angles of triangle is 180°28°+x+x=180°2x=180°-28°x=1522x=76°Hence ∠ABB=∠ADB=76°Now, ∠DAC is angle opposite to side DC and DC=AD=ABHence, ∠DAC=∠ABD=∠ADB=76°Now, ∠BAC=∠BAD+∠DAC                        =76°+28°                        =104°
Regards