Question

if ABCD is a paralellogram and angle 1 = angle 4 prove that angle DAB = angle DCB using axiom
PLEASE URGENT :C I need complete explanation

Answer 1

∠ABD=∠CDB=35

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Step-by-step explanation:

In parallelogram ABCD

AB=CD and AD=BC

AD is parallel to BC and side AB is parallel to CD

Angle DAB=85 degrees

Angle DBC=60 degrees

Angle DBC=Angle ADB=60 degree

Reason: Alternate interior angles are equal

In triangle ABD

\angle ABD+\angle ADB+\angle DAB=180∠ABD+∠ADB+∠DAB=180 degrees

Reason: Triangle angles sum property

85+60+\angle ABD=18085+60+∠ABD=180

145+\angle ABD=180145+∠ABD=180

\angle ABD=180-145=35^{\circ}∠ABD=180−145=35

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\angle ABD=\angle CDB=35^{\circ}∠ABD=∠CDB=35

∘

Reason: Alternate interior angles are equal.

Answer 2

∠ABD=∠CDB=35

∘

Step-by-step explanation:

In parallelogram ABCD

AB=CD and AD=BC

AD is parallel to BC and side AB is parallel to CD

Angle DAB=85 degrees

Angle DBC=60 degrees

Angle DBC=Angle ADB=60 degree

Reason: Alternate interior angles are equal

In triangle ABD

\angle ABD+\angle ADB+\angle DAB=180∠ABD+∠ADB+∠DAB=180 degrees

Reason: Triangle angles sum property

85+60+\angle ABD=18085+60+∠ABD=180

145+\angle ABD=180145+∠ABD=180

\angle ABD=180-145=35^{\circ}∠ABD=180−145=35

∘

\angle ABD=\angle CDB=35^{\circ}∠ABD=∠CDB=35

∘

Reason: Alternate interior angles are equal.