Hey guys..Prove that the bisects of 2 adjacent supplementary angles in

1.	Hey guys..Prove that the bisects of 2 adjacent supplementary angles include a right angle.Please solve this with proper figure..
Answer» Answer: 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° In Δ ABC, ∠ CAB + ∠ CBA + ∠ ABC = 180° (ANGLE Sum property) ⇒ 90° + ∠ ABC = 180° ⇒ ∠ ABC = 180° - 90° ⇒ ∠ ABC = 90° So, the bisectors of the two adjacent supplementary angles include a right angle. Hence proved. Step-by-step explanation: please mark me BRAINLIEST

Hey guys..Prove that the bisects of 2 adjacent supplementary angles include a right angle.Please solve this with proper figure..

Answer»

Answer:

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°

In Δ ABC,

∠ CAB + ∠ CBA + ∠ ABC = 180° (ANGLE Sum property)

⇒ 90° + ∠ ABC = 180°

⇒ ∠ ABC = 180° - 90°

⇒ ∠ ABC = 90°

So, the bisectors of the two adjacent supplementary angles include a right angle.

Hence proved.

Step-by-step explanation: