The side BC of triangle ABC is produced from ray BD CE is drawn parallel to AB Show that - Maths -

Question

The side BC of triangle ABC is produced from ray BD CE is drawn
parallel to AB Show that <ACD=<A+<B Also prove that
<A+<B+<C=180

Swagat Swargari · Accepted Answer

//draw the figure//

<ACE = <A (alternate angles)
<ECD = <B (corresponding angles)

So, <ACE + <ECD = <A + <B
or ACD = <A + <B (proved)

Again,
<ACE + <ECD + <C = <BCD
or <ACE + <ECD + <C = 180 (since BCD is a straight
line)
or <A + <B + <C = 180 (proved)

The side BC of triangle ABC is produced from ray BD.CE is drawn parallel to AB. Show that <ACD=<A+<B. Also prove that <A+<B+<C=180.