Question

Prove that if a ray stands on a line, then the sum of the adjacent angles so formed is ${180}^o$.

Answer 1

Given :

A ray CD which stands on a line.

AB such that $\angle ACD$ and $\angle BCD$ are formed.

To prove :

$\angle ACD+\angle BCD={180}^o$

Construction :

Draw ray $CE\perp AB$.

Proof :

$\angle ACD=\angle ACE+\angle ECD$ .........(1)

$\angle BCD=\angle BCE-\angle ECD$ .........(2)

Adding 1 and 2, we get,

$\angle ACD+\angle BCD=\angle ACE+\angle BCE$

$\angle ACD+\angle BCD={90}^o+{90}^o={180}^o$