Question

if one angle of a triangle is equal to the sum of other two,show that the triangle is a right-angled​

Answer 1

Given :-

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

To prove :-

• Show that the triangle is a right angled triangle

Proof :-

• Let other two angles are x and y

then, according to the question,(one angle is equal to sum of other two angles)

• one angle of triangle = x + y ....(i)

now, we know that

★ sum of all interior angles of a triangle is 180°

$\bold{: \implies x + y + (x + y) = 180 \degree} \\ \\ \bold{: \implies \:x + y + x + y = 180 \degree } \: \: \: \\ \\ \bold{: \implies 2x + 2y = 180 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 2(x + y) = 180 \degree } \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x + y = \cancel\frac{180 \degree}{2 \: } } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x + y = 90 \degree } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

➪ measure of x + y is 90°

and from (i) one angle = x + y

so that, one angle of the triangle is of 90°

therefore, the triangle is right angled triangle

hence, proved