Question

PQRS is a parallelogram . From information given in the figure,find the values of x and y.​

Answer 1

Given:-

• PQRS is a parallelogram
• ∠RSQ = 48°
• ∠PSR = 63°
• ∠RQS = 7y°
• ∠SQP = 4x°

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To Find:-

• Value of x
• Value of y

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Property Used:-

• Opposite side of a parallelogram are parallel.

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Solution:-

➥ As we know that opposite angles of a parallelogram are parallel;

So, PQ | | SR where SQ is a transversal.

Hence,

∠RSQ = ∠SQP ( Alternate interior angles)

➥ According to question;

48 = 4x

➜ x = 48 ÷ 4

➜ x = 12

∴x = 12

➥ Similarly,

According to property;

SP | | RQ where SQ is a transversal

Hence,

∠PSR = ∠RQS ( Alternate interior angles)

➥ According to question;

63 = 7y

➜ y = 63 ÷ 7

➜ y = 9

∴y = 9

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Answer:-

• Value of x is 12
• Value of y is 9

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Answer 2

$\mathtt{ \large{ \underline{ \boxed{ \purple{x = 12° , \: y = 9°}}}}}$

$\huge{ \underline{ \text{✿Solution}}}$

Here, given that,

PQRS is a parallelogram.

PQ // SR and SQ is a transversal.

$\sf{∴ ∠RSQ=∠PQS \: \: [ Alternate \: angles ]}$

$\sf{ = > 48{ \degree = 4x°}}$

$\sf{ = > x = \frac{48}{4} { \degree}}$

$\sf{ \orange{ \therefore{x = 12{ \degree}}}}$

Again,

SP // RQ and SQ is transversal.

$\sf{∴ ∠PSQ=∠RQS \: \: [ Alternate \: angles ]}$

$\sf{ = > 63{ \degree = 7y°}}$

$\sf{ = > y = \frac{63}{7} { \degree}}$

$\sf{ \orange{ \therefore{ y = 9 {\degree}}}}$

$\underline{ \rm{ \purple{Hence, \: x = 12{ \degree} \: and \: y = 9{ \degree}}}}$

❣Hope this helps you!!