Question

In given figure AB = AC and ACD = 120°, then find value of a

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Answer 1

Answer:

BAC=60°

Step-by-step explanation:

Given:- AB=AC

C=120°

BCA+ACD=180 ………linear angles

BCA+120=180

BCA=180-120

BCA=60°

BCA=CBA ………angles of isosceles triangle

CBA=60

ABC+ACB+BAC=180………sum of angles of triangle

60+60+BAC=180

120+BAC=180

BAC=180-120

BAC=60°

Answer 2

Answer:

Question:

In fig.,AB=AC and ∠ACD=120°.Find ∠A.

Answer:

We have,

AB=AC

➙∠B=∠C. [∵Angles opposite to equal sides are equal]

Now,∠ACB+∠ACD=180°. [Angles of a linear pair]

➙ ∠C+120°=180°

➙ ∠C=60°

➙ ∠B=60°. [∵∠B=∠C]

Using angle sum property in ∆ABC,we obtain

∠A+∠B+∠C=180°

➙ ∠A+60°+60°=180°. [∠B=∠C=60°]

➙ ∠A=60°