1. In triangle ABC, angle A = 30 and angle B = 60 . Point X is on side AC such that line segment BX bisects angle ABC . If AB=12, then find the area of triangle BXA .
2. Find the area of triangle PQR if PQ = QR=12 and angle PQR = 120.
3. In the diagram below,\(\angle PQR = \angle PRQ = \angle STR = \angle TSR, RQ = 8\) ,RQ = 8 , and SQ = 2. Find PQ.
4. In triangle XYZ, angle X=60 and angle Y = 45 . The bisector of angle X intersects YZ at W. If XW = 24, then find the area of triangle XYZ.
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Since triangle RQT is isosceles, we have\(ST = QT - QS = QR - QS = 8 - 2 = 6.\)