QS is the bisector of PQR and RS is the bisector of <PRQ. If <P = 76°, find the size of QSR.
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Answer:
∠ QSR = 128°
Step-by-step explanation:
∠ SRQ = ∠ PRS = 26° ( RS is angle bisector ) , then
∠ PRQ = 2 × 26° = 52°
∠ PQR = 180° - (52 + 76)° ← angle sum of Δ PQR
∠ PQR = 180° - 128° = 52°
∠ SQR = ∠ SQP = 26° ( QS is angle bisector )
Then
∠ QSR = 180° - (26 + 26)° = 180° - 52° = 128°