15. If two straight lines intersect each other then prove that the ray opprtieto the bisector of one of the angles so formed bisects the veráopposite angle.16. Prove that the bisectors of two adjacent supplementary anglesindalea right angle

15. If two straight lines intersect each other then prove that the ray

1.	15. If two straight lines intersect each other then prove that the ray opprtieto the bisector of one of the angles so formed bisects the veráopposite angle.16. Prove that the bisectors of two adjacent supplementary anglesindalea right angle
Answer» 16)Solution:-Given,∠ DAB + EBA = 180°. CA and CB are bisectors of∠DAB∠ EBA respectively.∴∠ DAC +∠ CAB = 1/2 (∠DAB).....(1)⇒∠ EBC +∠ CBA = 1/2 (∠ EBA)....(2)⇒∠ DAB +∠ EBA = 180°⇒ 2 (∠CAB) + 2 (∠ CBA) = 180° [using (1) and (2)]⇒∠ CAB +∠ CBA = 90°InΔ ABC,∠ CAB +∠ CBA +∠ ABC = 180° (Angle Sum property)⇒ 90° +∠ ABC = 180°⇒∠ ABC = 180° - 90°⇒∠ ABC = 90°So, the bisectors of the two adjacentsupplementary angles include a right angle.Hence proved.