Question

In the figure, PQ=QR=RS and angle PQR=128 . Find angle PTQ, angle PTS, angle ROS​

Answer 1

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 ∆PQR is isosceles

angle QRP = angle QPR = (180-128)/2

= 52/2

= 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°

Answer 2

Answer:

The angle ROS​ = 78°

Step-by-step explanation:

From the above question,

They have given :

PQ=QR=RS and angle PQR=128 .

Here we have to find,

The angle PTQ, angle PTS, angle ROS​.

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 ∆PQR is isosceles

angle QRP = angle QPR

                  = (180-128)/2

                  = 52/2

                  = 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°

The angle ROS​ = 78°

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