Prove that the bisectors of two adjacent supplementary angels include a right angle.

Hi!
Here is the answer to your question.
 
DAB + EBA = 180�
2CAB + 2CBA = 180� (Using (1) and (2))
⇒ ∠CAB + CBA = 90�
In ∆ABC,
CAB + CBA + ABC = 180� (Angle sum property)
90� + ABC = 180�
⇒ ∠ABC = 180� – 90� = 90�
Thus, the bisectors of two adjacent supplementary angles include a right angle.
 
Cheers!

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