Question

line DE parallel to line GF.ray EG and ray FG are bisectors of angle DEF and angle DFM resp

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Proof:

(3)

..(Sum of

s 180)

om (1) and (2)

ZDEF=ZEDGE GIF

From (3)

2=90

DEG ZGEF (Ray EG bisects ZDEF)

Let ZDEG=GEF=x

(1)

ZD FM=ZDF + ZFM

sures of all

(Angles addition postulate)

LDEF=x+

Form (1)

ZDEF=2

(2)

Line DE line GF

and line EF is the transversal

ZDEF LGFM (Corresponding angles)

/GFM=2x

From (2)1... (3)

4DFG /GFM (Ray FG bisects ZDFM)

ZDFG=2

From (3)]....(4)

(Angles addition postulate)

ZDFM-2r +21 From (3) and (4)

. ZDFM= 4x

(5)

DFM is an exterior angle of ADEF

.. ZDF=ZDF + ZDF

(Theorem of remote interior angles)

4x-4EDF+2r

/EDF= 4x-2r

EDF= 2/ DEG

[From (1)

Line DE line GF

(Given)

and line EG is the transversal

ZEDGE ZEDGE

.. (Alternate angles)