Question

Find the value of x,y,z,w in the given figure using suitable properties.
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Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ We are given a quadrilateral whose 3 angles are,

• 60°
• 80°
• 120°

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The value of x,y,z & w?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here we are gonna use the angle sum property,

✪ In a quadrilateral angles add up to 360°

✪ In a linear pair the Angles add up to 180°

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

So here on the way to finding w,

➝ $\displaystyle\sf 60^{\circ}+80^{\circ}+120^{\circ}+w' = 360^{\circ}$

➝ $\displaystyle\sf 260 + w' = 360^{\circ}$

➝ $\displaystyle\sf w' = 360-260$

➝ $\displaystyle\sf w' = 100^{\circ}$

So then w will be,

➝ $\displaystyle\sf w+w' = 180^{\circ} \:\:\{ Linear \ Pair\}$

➝ $\displaystyle\sf w+100 = 180^{\circ}$

➝ $\displaystyle\sf w = 180-100$

➝ $\displaystyle\sf \green{w = 80^{\circ}}$

Similarly x will be,

»» $\displaystyle\sf x'+x = 180^{\circ}\:\:\{ Linear \ Pair\}$

»» $\displaystyle\sf 120^{\circ}+x = 180^{\circ}$

»» $\displaystyle\sf x = 180-120$

»» $\displaystyle\sf \purple{x = 60^{\circ}}$

Value of y will be,

➢ $\displaystyle\sf y'+y = 180^{\circ} \:\:\{ Linear \ Pair\}$

➢ $\displaystyle\sf 80^{\circ}+y = 180^{\circ}$

➢ $\displaystyle\sf y = 180-80$

➢ $\displaystyle\sf \orange{y = 100^{\circ}}$

And finally the value of z will be,

➳ $\displaystyle\sf z'+z = 180^{\circ}\:\:\{ Linear \ Pair\}$

➳ $\displaystyle\sf 60^{\circ}+z = 180^{\circ}$

➳ $\displaystyle\sf z = 180-60$

➳ $\displaystyle\sf \pink{z = 120^{\circ}}$

Note : Here I've taken the adjacent angles of x as x', y as y', z as z' and w as w'

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Answer 2

straight lines have an angle of 180 degree

z = 180 - 60 = 120 degree

y = 180 - 80 = 100 degree

x = 180 - 120 = 60 degree

w = 180 - x (let x be the 4th angle in the quadrilateral

sum of all angles in a quadrilateral is 360 degree

360 = 120 + 80 + 60 + x

360 - 260 = x

x = 100

therefore w =180 - 100 = 80 degree

hope this helps you