Question

The valus of x and y in the given figure are *
2 points
Captionless Image
120, 45
130, 45
135, 45
145, 45​

Answer 1

Answer :

• 135 , 45

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Solution :

• In this figure , two terms are going to be used .

1. Vertically opposite angles : which means pair of opposite angles are equal which are inclined vertically .
2. Linear Pair : The sum of linear pair is always equal to 180° .

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» Solving further :

➪ $\sf \angle AOB \:=\: \angle y \:=\: 45°$

⠀⠀Reason : Vertically opposite angles

➪ $\sf \angle x \:+\: \angle y\:=\:180°$

➪$\sf \angle x\:+\:45°\:=\:180°$

➪ $\sf \angle x \:=\: 180°\:-\:45°$

➪ $\sf \angle x\:=\:135°$

⠀⠀⠀Reason : Linear pair

• Values of :

➪ $\sf \angle x\:=\:135° \:and\: \angle y \:=\:45°$

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Answer 2

$\bf \huge {\underline {\underline \red{AnSwEr}}}$

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Given

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• ∠MON = 45°

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To Find

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• Value of x and y

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Solution

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➨ ∠MON + ∠NOQ = 180° [ Linear Pair ]

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➨ 45° + x = 180°

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➨ x = 180° - 45°

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➨ x = 135°

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∠MON = ∠y = 45° [ Vertically Opposite Angle ]

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Therefore, x = 135° and y = 45°.

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Additionally

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• Vertically Opposite Angles are the angles opposite each other when two lines cross.

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• "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.

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• Two angles that are adjacent (share a leg) and supplementary (add up to 180°) is known as linear pair.