Question

The Sum of TWO Angles Of a triangle is equal to the third angle if the difference of the two Angles is 50° then third Angle is : a) 80° B) 90° c) 100° d) 70°​

Answer 1

answer is [b] 90°

let the 2 angles be x an

lets assume the third angle to be 90°

so that   x+y=90°

                     x-y=50°

by subtracting the 2 equations we get 2y = 40° and  

hence y= 20°

now by substituting y in any of the equations we get x = 70°

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

• The sum of two angles of a triangle is equal to the third angle.

• The difference of the two angles is 50°.

Let assume that

• First angle of a triangle = x°

• Second angle of a triangle = y°

• Third angle of a triangle = z°.

According to statement,

$\red{\rm :\longmapsto\:x + y = z - - - - (1)}$

We know,

Sum of all interior angles of a triangle is supplementary.

$\red{\rm :\longmapsto\:x + y + z = 180}$

On substituting the value of x + y, from equation (1), we get

$\red{\rm :\longmapsto\:z + z = 180}$

$\red{\rm :\longmapsto\:2z = 180}$

$\red{\rm\implies \:z = 90}$

Hence,

• Third angle of a triangle = z = 90°

So, Option (B) is correct.

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More to Know :-

Properties of a triangle

A triangle consists of three sides, three angles, and three vertices.

The sum of all internal angles of a triangle is always equal to 180°.

The sum of any two sides of a triangle is greater than the third side.

The side opposite to the greatest angle of a triangle is the largest side.

The angle opposite to longest side of a triangle is greater.

The angle opposite to equal sides are equal.

The side opposite to equal angles are equal.

The exterior angle of the triangle is equal to the sum of its interior opposite angles.