Question

If the three angles of a quadrilateral are 50° ,70° ,120°. find the 4th angle.​

Answer 1

Answer:

sum of angles in a quardilateral are 360

x+y+z+w=360

x=50 , y=70 , z=120 , w=?

50+70+120+w=360

120+120+w=360

w=360-240

w=120

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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

Hence, verified!

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Point to remember :

• L.H.S means left hand side
• R.H.S means right hand side