Isosceles triangle with angle bisector

In summary, the question is asking to find the measure of angle CBD in a triangle where ADB=65°, angle bisector bisects angle ADB, and the sum of all angles in a triangle is 180 degrees. The attempt at a solution involved finding the measure of angle ADB, which is 115 degrees. Therefore, the measure of angle CBD would be 180-115=65 degrees.
  • #1
Frank212
14
1

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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  • #2
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 ?
 
  • #3
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
 
  • #4
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
 

1. What is an isosceles triangle?

An isosceles triangle is a triangle with two equal sides and two equal angles.

2. What is an angle bisector?

An angle bisector is a line or ray that divides an angle into two equal parts.

3. How do you construct an isosceles triangle with angle bisector?

To construct an isosceles triangle with angle bisector, first draw a line segment with the desired length as the base of the triangle. Then, using a compass, draw two arcs from the endpoints of the base with the same radius, intersecting at a point above the base. Connect this point to the endpoints of the base to form the two equal sides of the triangle. Finally, draw a line from the point of intersection to the midpoint of the base, creating the angle bisector.

4. What is the relationship between the angle bisector and the sides of an isosceles triangle?

The angle bisector of an isosceles triangle divides the opposite side into two equal parts, creating two congruent triangles.

5. What is the measure of the angle bisector in an isosceles triangle?

The measure of the angle bisector in an isosceles triangle is half the measure of the vertex angle.

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