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If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

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A right triangle

An acute triangle

An isoceles triangle

None of the above

answer is A.

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Detailed Solution

Given that one angle is sum of other two angles of a triangle.
The sum of any triangle's three angles equals

180 °

.
Let

∆ ABC

be the required triangle.

⇒ ∠ A = ∠ B + ∠ C

…..

(1)

Now the sum of the angles is equal to 180°.

\Rightarrow ∠ A + ∠ B + ∠ C = 180 °

Substitute

(1)

in the above equation,

\Rightarrow ∠ A + ∠ A = 180 °

\Rightarrow 2 ∠ A = 180 °

\Rightarrow ∠ A = \frac{180}{2}

\Rightarrow ∠ A = 90 °

Here, one of the angle is equal to

90 °

. As a result,

∆ ABC

is a right angled triangle.
Thus, if one angle of a triangle is equal to the sum of the other two angles, then that triangle is right angled.
Therefore, option (1) is correct.

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