Question

PQ II ST,find values of x and y

Answer 1

the values of X and Y are 37° and 53°

QRS+QRT=180°
QRS+65=180
QRS=180-65
QRS=115

in ΔQRS
angles(Q+R+S)=180°
28+115+S=180°
143+S=180°
S=180-143
angleS=37°

now
angle QSR=PQS...(alternate angles)
therefore PQS=X=37°

in ΔPQS
P=90°
Q=37°
hence, S=y=53°

hope this helps

Answer 2

$\huge\mathbb{A~N~S~W~E~R}$

$<b>$

Here we have PQ || ST and SQ is transersal.

angle PQR = angle QRT (Alternate angle)

angle PQR = angle SQR + x

65° = 28° + x

x = 65° - 28° = 37°

$\boxed{x~=~37°}$

Here we have PQ || ST and PS is transversal.

angle P + angle PSR = 180°(interior

angles )

angle P + angle QSR + y = 180° ... (1)

Here PQ || ST and PS is transversal.

angle QSR = x ( alternte angles )

angle QSR = 28°

angle P + angle QSR + y = 180° ... (1)

90° + 37° + y = 90°

y = 180° - 90° - 37°

$\boxed{y~=~53°}$

${\large\color{Red}{x~=~37° }}$

${\large\color{Red}{y~=~53° }}$

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