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in triangle ABC, AB = AC and D is a point on line AC so that line BD bisects angle ABC. if BD = BC what is the measure, in degrees, of angle A?

 Aug 3, 2020
 #1
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Hi Guest, 

 

I believe this question has already been answered by CPhill here: https://web2.0calc.com/questions/geometry-help_68

 

For convenience sake, I have posted it here:

 

1) In triangle ABC, AB=AC and D is a point on line AC so that line BD bisects angle ABC. If BD=BC, what is the measure, in degrees, of angle A?

 

Call the each bisected angle. a

And call angle BCA, b

 

And since BD  = BC...then angle BDC  = angle BCD  = angle BCA  = b

 

So....since AB = AC....then angle ABC  = angle BCA ⇒  2a  = b ⇒  4a  = 2b

 

So..in triangle BDC....

 

a + 2b  =180

a + 4a  = 180

5a  = 180

a  = 36

 

And  b  = 2a =  72

 

So...in triangle ABC

 

Angle ABC  + Angle BCA  + Angle A  = 180

2a + b   +  Angle A  = 180

72  +  72  + Angle A  =  180

144  + Angle A  =  180

Angle A  =  180  - 144  =  108°

 

 

  This is all CPhill's work, so it is all his. 

 Aug 3, 2020
 #2
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A works out to 90 degrees.

 Aug 3, 2020
 #3
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in triangle ABC, AB = AC and D is a point on line AC so that line BD bisects angle ABC. if BD = BC what is the measure, in degrees, of angle A?

 

Let 1/2 of ∠ABC be an x

 

Hint:   The sum of angles in a triangle BCD is  5x, and ∠A = x  laugh

 Aug 3, 2020
edited by Dragan  Aug 3, 2020
edited by Dragan  Aug 3, 2020
 #4
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Thank you so much how do you like?

edit: i got 36

Guest Aug 4, 2020
edited by Guest  Aug 4, 2020
edited by Guest  Aug 4, 2020

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