Question

In the figure, PS 11, RQ 11, the degree measure of y is

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Answer 1

Answer:

hey mate.....

Step-by-step explanation:

▶️ Your answer is 80°...

Answer is in attachment...

Answer 2

Answer :-

• Measure of ∠PSR (y) = 80°

Given :-

• ∠SRX = 135°
• ∠PRQ = 55°
• ∠PSQ = 90°
• ∠PQR = 90°

To Find :-

• Measure of ∠PSR (y) = ?

Explanation :-

In order to find the measure OR value of 'y', we need to understand Exterior Angle Theorem.

• Exterior Angle Theorem - The exterior angle theorem states that if a triangle's side gets an extension, then the resultant exterior angle would be equal to the sum of the two opposite interior angles of the triangle.

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$\bf \bigstar \: In \: \triangle PQR,$

$\rm : \: \longrightarrow \angle PRQ + \angle PQR + \angle QPR = 180^\circ \qquad \bold{[Sum \: of \: all \: \angle \: in \: \triangle]}$

$\rm : \: \longrightarrow 55^\circ + \angle 90^\circ + \angle QPR = 180^\circ$

$\rm : \: \longrightarrow 145^\circ + \angle QPR = 180^\circ$

$\rm : \: \longrightarrow \angle QPR = 180^\circ - 145^\circ$

$\blue { \rm : \: \longrightarrow \angle QPR = 35^\circ }$

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$\bf \bigstar \: On \: \angle SPQ,$

$\rm : \: \longrightarrow \angle SPR + \angle QPR = \angle SPQ$

$\rm : \: \longrightarrow \angle SPR + 35^\circ = 90^\circ$

$\rm : \: \longrightarrow \angle SPR = 90^\circ - 35^\circ$

$\blue { \rm : \: \longrightarrow \angle SPR = 55^\circ }$

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$\bf \bigstar \: In \: \triangle PSR,$

$\rm : \: \longrightarrow \angle PSR + \angle SPR = \angle SRX \qquad \bold{[Exterior \: \angle \: Theorem]}$

$\rm : \: \longrightarrow Y + 55^\circ = 135^\circ$

$\rm : \: \longrightarrow Y = 135^\circ - 55^\circ$

$\red { \underline { \boxed { \bf : \: \longrightarrow Y = 80^\circ }}}$

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Hence, the measure of ∠PSR (y) is 80°.

@Agamsain