Question

if one angle of a triangle is equal to the sum of the other two angles, then show that triangle is right angled.

Answer 1

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Answer 2

Given,

One angle of a triangle is equal to the sum of the other two angles.

To Find,

Show that the triangle is right-angled.

Solution,

We can solve the question as follows:

It is given that one angle of a triangle is equal to the sum of the other two angles. We have to show that the triangle is right-angled.

Let us assume that the three angles of the triangle are x, y, and z. One of them is equal to the sum of the other two. Therefore,

$x = y + z$       ------- (1)

Now,

We know that the sum of all three angles of a triangle is equal to 180 degrees. The sum of x, y, and z will be 180.

$x + y + z = 180^{o}$

From equation (1),

$x + x = 180^{o}$

$2x = 180^{o}$

$x = \frac{180}{2} = 90^{o}$

One of the angles of the triangle is 90 degrees.

Hence, we have shown that the triangle is right-angled.