Angles inside a triangle

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P is a point inside triangle ABC such that 20° = ∠ABP , 10° = ∠PBC,
∠ ACP = 20° and ∠ PCB = 30°. Determine ∠CAP , in degree. No figure was given

I used the sine Law but the could not solve equations I got, I also tried making a point D on BP such that BD = CD to make us of the 10 degrees, but I still cant solve it.

geometry

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edited Jul 23 at 14:10

CiaPan

9,85311044

asked Jul 23 at 14:06

SuperMage1

663210

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up vote
2
down vote

favorite

1

P is a point inside triangle ABC such that 20° = ∠ABP , 10° = ∠PBC,
∠ ACP = 20° and ∠ PCB = 30°. Determine ∠CAP , in degree. No figure was given

I used the sine Law but the could not solve equations I got, I also tried making a point D on BP such that BD = CD to make us of the 10 degrees, but I still cant solve it.

geometry

share|cite|improve this question

edited Jul 23 at 14:10

CiaPan

9,85311044

asked Jul 23 at 14:06

SuperMage1

663210

add a comment | 

up vote
2
down vote

favorite

1

up vote
2
down vote

favorite

1

1

P is a point inside triangle ABC such that 20° = ∠ABP , 10° = ∠PBC,
∠ ACP = 20° and ∠ PCB = 30°. Determine ∠CAP , in degree. No figure was given

I used the sine Law but the could not solve equations I got, I also tried making a point D on BP such that BD = CD to make us of the 10 degrees, but I still cant solve it.

geometry

share|cite|improve this question

edited Jul 23 at 14:10

CiaPan

9,85311044

asked Jul 23 at 14:06

SuperMage1

663210

P is a point inside triangle ABC such that 20° = ∠ABP , 10° = ∠PBC,
∠ ACP = 20° and ∠ PCB = 30°. Determine ∠CAP , in degree. No figure was given

I used the sine Law but the could not solve equations I got, I also tried making a point D on BP such that BD = CD to make us of the 10 degrees, but I still cant solve it.

geometry

share|cite|improve this question

edited Jul 23 at 14:10

CiaPan

9,85311044

asked Jul 23 at 14:06

SuperMage1

663210

share|cite|improve this question

share|cite|improve this question

edited Jul 23 at 14:10

CiaPan

9,85311044

edited Jul 23 at 14:10

CiaPan

9,85311044

edited Jul 23 at 14:10

CiaPan

9,85311044

9,85311044

asked Jul 23 at 14:06

SuperMage1

663210

asked Jul 23 at 14:06

SuperMage1

663210

asked Jul 23 at 14:06

SuperMage1

663210

663210

add a comment | 

add a comment | 

1 Answer
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Extend BP so that it intersects AC at D and extend CP so that it intersects AB at E. Now consider triangle ADP and triangle AEP these triangle are congruent so angle APD =70 and angle DEC=40 APD+DEC=APC=110 Hence angle CAP=30

share|cite|improve this answer

edited Jul 23 at 14:31

answered Jul 23 at 14:21

dank uploader

13

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How do we know that triangles ADP and AEP congruent?
  – saulspatz
  Jul 23 at 14:34
  

  
  
  
  

add a comment | 

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1 Answer
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1 Answer
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active

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up vote
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Extend BP so that it intersects AC at D and extend CP so that it intersects AB at E. Now consider triangle ADP and triangle AEP these triangle are congruent so angle APD =70 and angle DEC=40 APD+DEC=APC=110 Hence angle CAP=30

share|cite|improve this answer

edited Jul 23 at 14:31

answered Jul 23 at 14:21

dank uploader

13

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How do we know that triangles ADP and AEP congruent?
  – saulspatz
  Jul 23 at 14:34
  

  
  
  
  

add a comment | 

up vote
0
down vote

Extend BP so that it intersects AC at D and extend CP so that it intersects AB at E. Now consider triangle ADP and triangle AEP these triangle are congruent so angle APD =70 and angle DEC=40 APD+DEC=APC=110 Hence angle CAP=30

share|cite|improve this answer

edited Jul 23 at 14:31

answered Jul 23 at 14:21

dank uploader

13

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How do we know that triangles ADP and AEP congruent?
  – saulspatz
  Jul 23 at 14:34
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

Extend BP so that it intersects AC at D and extend CP so that it intersects AB at E. Now consider triangle ADP and triangle AEP these triangle are congruent so angle APD =70 and angle DEC=40 APD+DEC=APC=110 Hence angle CAP=30

share|cite|improve this answer

edited Jul 23 at 14:31

answered Jul 23 at 14:21

dank uploader

13

Extend BP so that it intersects AC at D and extend CP so that it intersects AB at E. Now consider triangle ADP and triangle AEP these triangle are congruent so angle APD =70 and angle DEC=40 APD+DEC=APC=110 Hence angle CAP=30

share|cite|improve this answer

edited Jul 23 at 14:31

answered Jul 23 at 14:21

dank uploader

13

share|cite|improve this answer

share|cite|improve this answer

edited Jul 23 at 14:31

edited Jul 23 at 14:31

edited Jul 23 at 14:31

answered Jul 23 at 14:21

dank uploader

13

answered Jul 23 at 14:21

dank uploader

13

answered Jul 23 at 14:21

dank uploader

13

13

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How do we know that triangles ADP and AEP congruent?
  – saulspatz
  Jul 23 at 14:34
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How do we know that triangles ADP and AEP congruent?
  – saulspatz
  Jul 23 at 14:34
  

  
  
  
  

How do we know that triangles ADP and AEP congruent?
– saulspatz
Jul 23 at 14:34

How do we know that triangles ADP and AEP congruent?
– saulspatz
Jul 23 at 14:34

add a comment | 

 

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