Isosceles triangle with angle bisector

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SUMMARY

The discussion centers on solving for angle CBD in an isosceles triangle using the angle bisector theorem. The angles ADB and CBD are calculated, with ADB totaling 180 degrees. The correct measure for angle CBD is established as 115 degrees, derived from subtracting 65 degrees from 180 degrees. The confusion arises from the incorrect interpretation of the angle bisector, which divides an angle into two equal parts.

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Frank212
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Homework Statement


Find x[/B]
bandicam 2016-08-12 23-30-16-190.jpg


Homework Equations


a+b+c=180[/B]

The Attempt at a Solution


ADB= 65+65+50=180
How do I find x in DBC?
 
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Frank212 said:

Homework Statement


Find x[/B]
View attachment 104594

Homework Equations


a+b+c=180[/B]

The Attempt at a Solution


ADB= 65+65+50=180
How do I find x in DBC?
What is the measure of angle CBD ?
 
SammyS said:
What is the measure of angle CBD ?
SammyS said:
What is the measure of angle CBD ?

ADB=50+65+65=180
angle bisector -> angle on a line 180 degrees. 180-65=115
x= 180-115=65, 65/2=32.5
CBD=32.5+115+32.5

x=32.5
 
Frank212 said:
ADB=50+65+65=180
angle bisector -> angle on a line 180 degrees. 180-65=115
x= 180-115=65, 65/2=32.5
CBD=32.5+115+32.5

x=32.5
Actually, I asked about angle CBD, ( ∠ CBD ), not triangle CBD ( Δ CBD ).

Maybe, that's what you mean by
" angle bisector -> angle on a line 180 degrees. 180-65=115 ",​
but an angle bisector cuts an angle exactly into two angle of equal measure.

So, yes, .∠ CBD = 180° - 65° = 115° .

It's really very confusing, and incorrect, when you state the following.
Frank212 said:
CBD=32.5+115+32.5
 

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