Determine the value of x in the triangle with its interior angles given below.

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25 ∘

27 ∘

29 ∘

31 ∘

answer is A.

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Detailed Solution

Here, we are given a triangle with its interior angle measures in terms of variable x.
We have to determine the value of x.
So, we know that the sum of all the interior angles of a triangle is always

180 ∘

, by the angle sum property.
So, applying this property on

△ A B C

, we get,

∠ A + ∠ B + ∠ C = 180 ∘ x + 10 ∘ + 3 x + 5 ∘ + 2 x + 15 ∘ = 180 ∘ 6 x + 30 ∘ = 180 ∘ 6 x = 180 ∘ − 30 ∘ 6 x = 150 ∘ x = 150 ∘ 6 x = 25 ∘

Hence, the correct option is (1).

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