Prove that the bisectors of two adjacent supplementary angels include a right angle.
Hi!
Here is the answer to your question.
∠DAB + ∠EBA = 180�
⇒ 2∠CAB + 2∠CBA = 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!