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In $Δ A B C$ , $A B = A C$ and $∠ A = 70 °$ , then from the following choices, the value of $∠ C$ is-

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55 °

35 °

75 °

45 °

answer is A.

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Detailed Solution

It is given that in

Δ A B C

A B = A C

.
and

∠ A = 70 °

.
We have to find the

∠ C

.
Consider

Δ A B C

A B = A C

angles opposite to equal sides are equal, so

∠ B = ∠ C

......(1)
Calculate

∠ C

.
By angle sum property of the triangle,

∠ A + ∠ B + ∠ C = 180 °

Since

∠ B = ∠ C

70 ° + 2 ∠ C = 180 °

2 ∠ C = 180 ° − 70 °

∠ C = 110 ° 2

∠ C = 55 °

Therefore, the measure of

∠ C

55 °

.
Hence option 1 is correct.

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