Q. 65.0( 2 Votes )

# Let’s write the measurement of ∠ACB and ∠BAC if AB = AC.

Answer :

Given: ΔABC, ∠ABC = 70° and AB = AC

To find the measurement of ∠ACB and ∠BAC

Now in ΔABC, it is given AB = AC

We know angles opposite to equal sides are equal, therefore

⇒∠ACB = ∠ABC

Substituting given value in the above equation, we get

⇒∠ACB = 70°…….(i)

We also know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

∠BAC + ∠ACB + ∠ABC = 180°

Substituting the values from equation(i) and given criteria, we get

∠BAC + 70° + 70° = 180°

⇒ ∠BAC = 180° - 70° - 70°

⇒ ∠BAC = 40°

From equation (i) and (ii), the required values of the angles are

∠ACB = 70° and ∠BAC = 40°

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