Question

In the given figure, PQ=QR=RS and /_PQR=128. Find /_PTQ, /_PTS, and /_ROS.

Answer 1

Step-by-step explanation:

We have PQ = QR hence ∠QPR = ∠QRP

Also ∠PQR + ∠QPR + ∠QRP = ∠180º (sum of interior angles of a triangle).

∠PQR = 128º

∠QPR = ∠QRP = 180 - 128 / 2 = 26º

We can say that ∠QSR and ∠QPR are angles in the same segment, then:

∠QSR = ∠QPR = 26º

Now in triangle QRS, since QR = RS hence ∠QRS = ∠SQR = 26º

Also ∠QRS = 180º - 26 - 26º = 128º

Then ∠ROS = 2∠SQR = 2 x 26º = 52º

Also we can say that ∠QRS + ∠QTS = 180º, then ∠QTS = 180º - 128º = 52º

From the figure we also know that: ∠PQS + ∠SQR = ∠PQR

Then:

∠PQS = 128º - 26º = 102º

Now in cycic quadrilateral PQST, ∠PQS + ∠PTS = 180º

Then:

∠PTS = 180º - 102º = 78º

Now we can say that

∠PTQ + ∠QTS = ∠PTS

∠PTQ = 78º - 52º = 26º

Hence the angles measurement is 26º

Bro Please mark it as the brainliest