Question

the thre,e angle of a quadrilateral are 60°,80° and 120°,find the south angle​

Answer 1

Correct Question :-

The three angles of a quadrilateral are 60° , 80° and 120° , Find the 4th angle?

Solution :-

Here,

A quadrilateral is given whose three angles are 60° , 80° , 90° but we have to find the fourth angle .

Let the fourth angle be x

Therefore,

We know that,

Sum of angles of quadrilateral = 360°

Subsitute the required values,

60° + 80° + 120° + x = 360°

140° + 120° + x = 360°

260° + x = 360°

x = 360° - 260°

x = 100°

Hence, The fourth angle of the given quadrilateral is 100° $.$

Formula :-

For finding the sum of angles of any polygon we always use the formula = 180(n - 2 )

n is the number of sides of polygon

For Example :- quadrilateral

Sum of angles of quadrilateral

= 180( 4 - 2 )

= 180 * 2

= 360°

Hence, proved

Answer 2

Given :

Three angles of a quadrilateral are 50°, 70° and 120°.

To Find :

The measure of fourth angle.

Conception :

Here, we are provided with three angles of a quadrilateral which are 50°, 70° & 120°. And we have to find the measure of fourth angle.

Supposition: Let us suppose the fourth angle as 'x'

As we know that,

$\underline{ \underline{ \boxed{ \tt{Sum \: of \: all \: angles_{(Quadrilateral)} = 360^{\circ} }}}}$

And by substituting values, we will find the measure of fourth angle.

Calculations :

We know that,

$\underline{ \underline{ \boxed{ \tt{Sum \: of \: all \: angles_{(Quadrilateral)} = 360^{\circ} }}}}$

Putting the values in the equation,

$\rightarrow\bf{50^{\circ} + 70^{\circ} + 120^{\circ} + x^{\circ} = 360^{\circ}}$

On adding up the numbers,

$\rightarrow\bf{240^{\circ} + x^{\circ} = 360^{\circ}}$

Transposing x to L.H.S and 240° to R.H.S, changing the sign and performing subtraction.

$\rightarrow\bf{x^{\circ} = 360^{\circ}} - 240^{\circ}$

On subtracting the numbers,

$\rm\longrightarrow{\pink{\underbrace{\boxed{\blue{\bf{ x^{\circ} = 120^{\circ}}}}}}}$

Therefore, the measure of fourth angle is 120°.

Verification :

We know that sum of all angles of a quadrilateral sum up to 360°. And the angles are 50°, 70°, 120° & 120°. So let's check whether they are summing up to 360° or not.

$\rightarrow\bf{50^{\circ} + 70^{\circ} + 120^{\circ} + 120^{\circ} = 360^{\circ}}$

By adding the numbers,

$\rightarrow\bf{120^{\circ} + 240^{\circ} = 360^{\circ}}$

On adding 120° with 240°

$\rightarrow\bf{360^{\circ} = 360^{\circ}}$

$\therefore$ L.H.S = R.H.S