Question

a triangle has sides QP and RQ of triangle PQR are produced to points S and T respectively if<SPR=135° and <PQT=110°, find <PRQ​

Answer 1

∠ PRQ = 65°

Explanation:

See the diagram attached.

The ∠ PQR and ∠ PQT are supplementary.

So, ∠ PQR = 180° - 110° = 70° {Since given that ∠ PQT = 110°}

Again, ∠ SPR and ∠ RPQ are supplementary.

So, ∠ RPQ = 180° - 135° = 45° {Since, given that ∠ SPR = 135°}

Now, from Δ PQR, ∠ PQR + ∠ RPQ + ∠ PRQ = 180°

⇒ 70° + 45° + ∠ PRQ = 180°

⇒ ∠ PRQ = 180° - 70° - 45° = 65° (Answer)