Question

4. The sum of two angles of a triangle is equal to its third angle. Find the third
angle ​

Answer 1

$\bold{\underline{\underline{Answer:}}}$

Third angle = 90°

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :

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

To find :

• Third angle

Solution :

Let the first angle be x

Let the second angle be y

Let the third angle be c

$\bold{\underline{\underline{As\:per\:the\:question:}}}$

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

Constitute it mathematically,

$\implies$ $\bold{a+b=\:c}$ ---> (1)

We know that : Sum of measures of all angles in a triangle is 180°

$\implies$ $\bold{a+b+c=180}$

Substituting value of c from (1),

$\implies$ $\bold{a+b+a+b=180}$

$\implies$ $\bold{a+a+b+b=180}$

$\implies$ $\bold{2a+2b=180}$

Considering 2 as common,

$\implies$ $\bold{2(a+b)=180}$

$\implies$ $\bold{a+b\:={\frac{180}{2}}}$

$\implies$ $\bold{a+b=90}$

But, a + b = c

[As per the given condition in the question]

•°• Third angle = c = 90°

Answer 2

$\huge\mathfrak{\underline{\underline{Answer:-}}}$

Sum of two angles of a traingle is equal to its third angle.

According to Triangle Property , the sum of all the angles in a traingle is 180°.

Let the angles be x , y and z.

We know that - x and y are equal (x = y)

- The sum of x+y is equal to z (x+y = z or 2x = z )

We need to find the third angle.

According to problem ,

x + y + (x + y) = 180°

x + y + x + y = 180°

2x + 2y = 180°

2 ( x + y) = 180°

x + y = 180/2

x + y = 90°

As z = x + y

The third angle is 90°