Question

15. In the given figure, Find the value of x, y and z
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Answer 1

★ How to do :-

Here, we are given with the diagram which has two lines that intersect each other. We are given with the measurement of one of the angles in it and the other three angles are named as x, y and z. We are asked to find the value of those unknown angles. So, here we are going to use the concepts of vertically opposite angles amd also the concept of that the angles forming a straight line always measures 180° when added. So, let's solve!!

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➤ Solution :-

We know that two angles that forms a straight line always measures 180° when added. So,

Value of ∠x :-

${\tt \leadsto \angle{x} + {120}^{\circ} = {180}^{\circ}}$

${\tt \leadsto \angle{x} = {180}^{\circ} - {120}^{\circ}}$

${\tt \leadsto \orange{\underline{\boxed{\tt \angle{x} = {60}^{\circ}}}}}$

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We know that two angles that forms a straight lime always measures 180°. So,

Value of ∠y :-

${\tt \leadsto \angle{y} + {60}^{\circ} = {180}^{\circ}}$

${\tt \leadsto \angle{y} = {180}^{\circ} - {60}^{\circ}}$

${\tt \leadsto \orange{\underline{\boxed{\tt \angle{y} = {120}^{\circ}}}}}$

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We know that two angles that forms a straight line always measures 180°. So,

${\tt \leadsto \angle{z} + {120}^{\circ} = {180}^{\circ}}$

${\tt \leadsto \angle{z} = {180}^{\circ} - {120}^{\circ}}$

${\tt \leadsto \orange{\underline{\boxed{\tt \angle{z} = {60}^{\circ}}}}}$

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Hence solved !!

Answer 2

To find :

• The values of x ,y , z

Approach :

• So,in the given question we need to work with the concept of lines and angles.
• Concept to be used are :
• ➭ Vertical opposite angles
• ➭ Sum of angles formed on straight line = 180°or the concept of linear pair.

So, let's proceed with solution :

➠ Let ∠1 = 120° { given }

➨ ∠y = ∠1 { vertically opposite angles}

➨ ∠y = 120°

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➨ ∠y + ∠x = 180° {Linear pair }

➨ 120° + ∠x = 180°

➨ ∠x = 180 - 120

➨ ∠x = 60°

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➨ ∠x = ∠z {Vertically opposite angles }

➨ ∠z = 60°

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✦ Therefore, ∠x = 60°, ∠y =120° , ∠z = 60°