Answer:

Though it is not given, I am assuming on the basis of image that the Pentagon is enclosed by a circle and that O is centre of the circle.

PQ = QR

so APQR is isosceles

angle QRP

[tex]= angle \: QPR ( \frac{180 - 128}{2} )[/tex]

[tex] = \frac{52}{2} [/tex]

= 26°

now chord QR makes an angle of 26° at a point on circumference. so it will make 26*2 = 52° at centre.

now equal chords make equal angle at centre or

circumference.

angle POQ = angle QPR = angle ROS = 52°

now chord PQ makes an angle of 52° at centre, so it will make angle of 26° at circumference.

so, angle PTQ = 26°.

Again, each of the chords will make an angle of 26°.

at any point on circumference and hence on point T

also.

so angle PTS = PTQ + QTR + RTS

= 26 + 26 + 26

= 78°

Step-by-step explanation:

[tex]hope \: it \: helps \: u \: bro[/tex]

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