Question

In a pentagon pqrst ,pq=QR=RS and angle pqr=128, find angle ptq and angle pts

Answer 1

Answer:

The angles measurement is 26º.

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.

Answer 2

Angle PTQ is 128° and angle PTS is 64°.

• A pentagon is a two-dimensional geometric shape with five sides and five angles. When the two sides of a pentagon have a common point, an angle is created. The number of angles in a pentagon is five since there are five vertices in a pentagon. A closed pentagon has five sides and five angles and is a two-dimensional polygon. Different varieties of pentagons can be identified based on their characteristics.
• Regular pentagons are those with equal sides and interior angles. An irregular pentagon is one that does not have equal sides on all sides and does not have equal interior angles.

Here, according to the given information, we are given a regular pentagon.

Then, angle PTQ is also equal to the interior angle given that is 128 degrees.

Then angle PTS will be, $\frac{128}{2}=64$.

hence, angle PTQ is 128° and angle PTS is 64°.

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