If triangle PQR has $\angle P = 120^\circ$ and PQ = PR, then $\angle Q$ and $\angle R$ will be respectively:

Explanation

Diagram of a triangle with vertices P, Q, R showing angle P as 120 degrees and sides PQ and PR marked as equal ∵ In $\Delta$PQR $\angle P = 120^\circ$ and PQ = PR ∴ If two sides of a triangle are equal, then the angles opposites to it will also be. ∴ $\angle Q = \angle R$ ...........(i) ∵ $\angle P + \angle Q + \angle R = 180^\circ$ ∴ $120 + \angle Q + \angle Q = 180^\circ$ (∵ From eqⁿ (i) $\angle Q = \angle R$) $2\angle Q = 180^\circ - 120^\circ$ $2\angle Q = 60^\circ$ $\angle Q = 30^\circ$ ∴ $\angle R = 30^\circ$