Question

In the given figure, PQR is a triangle with side PR produced to S and RT || PQ
Find the marked angles.​

Answer 1

Answer:

In ΔPQR, we have

PQ=PR⇒∠R=∠Q

Now, ST∥QR.

⇒∠PST=∠PQR and ∠PTS=∠PRQ     [∵ Corresponding angles are equal]

⇒∠PST=∠Q and ∠PTS=∠R

⇒∠PST=∠PTS

⇒PT=PS

Answer 2

y + x + 80° = 180° ( linear pair).

so y + x = 100°

PQ is Parralel to RT.

then, angle x = angle Z

Now in ∆ PQR.

angle z + angle y + 70° = 180°

110 + 70 = 180°

x + y = 100 ............... ( eq. 1 ).

X = 70°

y = 30°

z = 80°

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