Question

in the given figure AB//DE prove that angleABC+angleBCD=180+angleCDE

Answer 1

RTP: LABC+ LBCD = 180°+LCDE

construction: drawing a line GH through C ll to DE and AB, extending B to I and D to J

Proof: LGCD=LCDE }
LGCB=LIBC } (alternate interior angles)
LABC=LBCH }

LGCB+LGCD=LBCD (shown above)
LGCB+LCDE=LBCD (putting LCDE in LGCD)
LABC+LGCB=180° (co interior angles)
LABC+LGCB+LCDE=180°+LCDE (adding LCDE on both the sides)
LABC+LBCD=180°+LCDE.
hence proved.

Answer 2

Answer:

Step-by-step explanation:

RTP: LABC+ LBCD = 180°+LCDE

construction: drawing a line GH through C ll to DE and AB, extending B to I and D to J

Proof: LGCD=LCDE }

LGCB=LIBC } (alternate interior angles)

LABC=LBCH }

LGCB+LGCD=LBCD

LGCB+LCDE=LBCD (putting LCDE in LGCD)

LABC+LGCB=180° (co interior angles)

LABC+LGCB+LCDE=180°+LCDE (adding LCDE on both the sides)

LABC+LBCD=180°+LCDE.

hence proved.