Question

In the given figure, if QP|| SR, then find the value of a.

Answer 1

Answer:

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Step-by-step explanation:

We will construct LM such that LM ∣∣ PQ ∣∣ SR

Here, LM parallel to QP and QT is a transversal.

∴∠LTQ=∠PQT --------- [∵alternate angles]

⇒∠LTQ=60° --------- (1)

Also, LM parallel to SR and TS is a transversal.

∴∠TSR=∠LTS ---------- [∵alternate angles]

⇒∠LTS=30° -------- (2)

From equation 1 and 2, we get

a=∠LTQ+∠LTS=60° + 30° = 90°