It is known that the triangle ABP angle PAE= 10 degree angle BAE=70 degree angle PBD=20 degree angle ABD=60 degree.

Discovery: angle DEA= angle C=?

Solution: Make an equilateral triangle PBF with PB as the side to the left, connect EF, and make an equilateral triangle EG with EF as the side to connect AG, AF and DF.

So PB=PF=BF.

BPF angle = PFB angle = PBF angle =60 degrees.

FE=FG=EG

EFG angle = FEG angle = FGE angle =60 degrees.

Because angle PAB= angle PAE+ angle BAE

Angle PAE= 10 degree

Angle BAE=70 degrees

So the angle PAB=80U shielding.

Because angle PBA= angle PBD+ angle ABD

PBD angle =20 degrees

Angle ABD=60 degrees

So the angle PBA=80 degrees

So angle PAB= angle PBA=80 degrees.

So PA=PB

So PA=PF=BF

So angle PAF= angle PFA

Because angle PAB+ angle PBA+ angle APB= 180 degrees.

So the angle APB=20 degrees

Because angle APF= angle BPF- angle APB=60-20=40 degrees.

Angle APF+ Angle PAF+ Angle PFA= 180 degrees.

So PAF angle PFA angle =70 degrees.

Because angle APB= angle PBD=20 degrees (proved)

So PD=BD

Because PF=BF (authentication)

DF=DF

So triangle PFD and triangle BFD are congruent (SSS)

So angle PFD= angle BFD= 1/2 angle PFB=30 degrees.

So angle ADF= angle APF+ angle PFD=40+30=70 degrees.

So angle ADF= angle PAF=70 degrees.

So AF=DF

Because angle ADF+ angle PAF+ angle AFD= 180 degrees.

So the angle AFD=40 degrees

Because angle BFA= angle PFA- angle PFB=70-60= 10 degrees.

So angle BFA= angle PAE= 10 degrees.

Because angle ABF= angle PBA- angle PBF=80-60=20 degrees.

So ABF angle APB angle =20 degrees.

Because BF=PA (authentication)

So triangle ABF and triangle EPA are congruent (ASA)

So AE=AF

So angel ·AEF = angel ·AFE

Because angle EAF= angle PAF+ angle PAE=70+ 10=80 degrees.

Angle electric arc furnace+angle AEF+ angle AFE= 180 degrees.

So AEF angle = AFE angle =50 degrees.

Because AE=AF (authentication)

AG=AG

FG=EG (certification)

So triangle age and triangle AGF congruence (SSS)

So angle AGF= angle AGE= 1/2 angle FGE=30 degrees.

Because angle AFG= angle EFG- angle AFE=60-50= 10 degrees.

Angle DFE= angle AFE- angle AFD=50-40= 10 degree.

So the angle AFG= the angle DFE= 10 degrees.

Because FE=FG (authentication)

DF=AF (authentication)

So triangle DFE and triangle AFG are congruent (SAS).

So the angle AFG= the angle DEF=30 degrees.

Because angle DEA= angle AEF- angle DEF=50-30=20 degrees.

Angle DEA= angle c

So the angle C=20 degrees.