Question

In Fig., AB = AC and ∠ACD = 105°, find ∠BAC.

Answer 1

Given,

AB = AC

∠ACD = 105°

Since,

∠BCD = 180°(Straight angle)

∠BCA + ∠ACD = 180°

∠BCA + 105° = 180°

∠BCA = 75°(i)

Now,

ΔABC is an isosceles triangle

∠ABC = ∠ACB (Angle opposite to equal sides)

From (i), we have

∠ACB = 75°

∠ABC = ∠ACB = 75°

Sum of interior angle of triangle = 180°

∠A +∠B +∠C =180°

∠A = 180° - 75° -75°

= 30°

Therefore,

∠BAC = 30°