Prove that the bisectors of 2 adjacent supplementary angles include a right angle?

Answer 1

∠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.