Question

I am not understanding this problem ​

Answer 1

Step-by-step explanation:

<P +<R+<T = 180° ( sum of < s property )

95°+40°+<T = 180°

<T= 180°-135°

<T = 45°

<T = <STQ = 45° ( vert . oppo <s )

In ∆TSQ

<STQ+<TSQ+ <SQT = 180° ( sum of all <s property )

45° + 75°+ <SQT = 180°

<SQT = 180°-120°

<STQ= 60°

Given : if PQ perpendicular to PS so ∆ PSQ is a right ∆ at P and PQ //SR

<SQR = 28°

and

<QRT = 65°

<QRT+ <QRS = 180° ( ST is a straight line )

65° + <QRS= 180°

<QRS = 115°

IN ∆ QSR

<QRS +<SQR + <QSR = 180° ( sum of all <s property

115°+28° + <QSR = 180°

<QSR = 180° - 143

<QSR = 37°

<PQS = QSR = 37° ( alt . int oppo . angle )

IN ∆ PSQ

<PQS + <PSQ = 90° (PSQ is a right triangle)

37°+ <PSQ = 90

<PSQ = 53°

so x= 37° and y = 53°

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