Please help me solve the 51st question

Please help me solve the 51st question Long Answer Questions 47. Prove that iftwo lines intersect each other, then the vertically opposite angles are equal 48. If two parallel lines are intersected by a transversal, prove that the bisectors of rhe interior angles on the same side of transversal intc.sect each other al right angles. 49. Prove that if arms of an angle are respectively parallel to the arms of 50. 51. 52. another angle, then the angles are either equal or supplementary. In Fig. 6.66, PT -L QR and PS is the bisector of ZP. If 260' and LR 30', find ZTPS. Fig'" In Fig. 6.07, bisector of ZB and ZD ofa quadrilateral ABCD meet CD and AB produced at PBiQ respectively. Prove Z-P + ZQ = — (Z•IBC + ZADC). Fig 6.67 In Fig. 6å58, show that + 3600. 53. Prove that the sum of the angles ofa triangle is 1800. SELF-ASSESSMENT TEST Time : 45 minutes Fig. . many triangles can be dra;sn haung answer 7. In Fig. 6.72,ltli12 S. lnHg.6.73.ifABliCD.APQzTandPK 9. In Ftg- 6.74, lines.4B and CDinters.e€tat reflex LEOC..

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