Question

in the figure given below ,if PQ is parallel to RS and PXM=50 and MYS=120,find the value of x

Answer 1

Step-by-step explanation:

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Answer 2

The value of x = 270°

Given:

PQ || RS and the measure of ∠PXM = 50° and ∠MYS = 120°

To find:

The value of x

Solution:

Draw a line AB through M

Here, M will parallel to PQ and RS

⇒ Angle ∠BMX = 50°    [ ∵ ∠PMX and ∠BMX are alternate angles ]

From straight line RYS

⇒ ∠RYM + ∠SYM= 180°

⇒ ∠RYM = 180° - ∠SYM

= 180° - 120° = 60°

⇒ ∠RYM = 60°

Here, ∠RYM will be alternative angle to ∠BMY

⇒ ∠BMY =  60°  

From above data,

∠XMY =  ∠BMX +∠BMY

= 50° + 60° = 110°

⇒  ∠XMY = 110°

As we know at point A the angle = 360°  then  

⇒ (x-20)° + ∠XMY = 360°

⇒ x - 20° + 110° = 360°

⇒ x - 90° = 360°

⇒ x = 270°

[ for more understanding observe the given picture ]

The value of x = 270°

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