Question

In Fig. 10.24, AB = AC and ∠ACD = 105°, find ∠BAC.

Answer 1

Given :  AB = AC and ∠ACD = 105°

∠BCA + ∠ACD = 180°

[Angles of a linear pair]

∠BCA + 105°= 180°

∠BCA = 180° - 105°

∠BCA = 75° ………….(1)

Now,

Δ ABC is an isosceles triangle :  

AB = AC

∠ABC = ∠ACB  

[Angles opposite to equal sides are equal]

From eq (1),  

∠ABC = ∠ACB = 75°

We know, that the sum of angles in a triangle is 180°.  

∠A + ∠B + ∠C = 180°

∠A + 75°+ 75° = 180°

∠A + 150° = 180°

∠A = 180° - 150°  

∠A = 30°

Hence, ∠BAC is 30°.

HOPE THIS ANSWER WILL HELP YOU…..

 

 

Similar questions :

In a Δ ABC, if ∠A =120° and AB=AC. Find ∠B and ∠C.

brainly.in/question/15907313

 

Determine the measure of each of the equal angles of a right angled isosceles triangle.

OR

ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

https://brainly.in/question/15907312