What is the size of angle ABE?

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In summary, In a triangle ABC, angle BAC is 35 degrees. D is a point on AB such that AD=BC and angle ADC=110 degrees. E is a point on AC such that BE=DC. By drawing and identifying isosceles triangles, it is determined that the size of angle ABE is 40 degrees.
  • #1
chickenguy
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hi everyone, there si this problem that i can't figure out and i was looking for some help
FIND THAT ANGLE!

In a triangle ABC, angleBAC=35*, D is a point on AB such that AD=BC and angle ADC=110*. E is a point on AC such that BE=DC. What is the size of angle ABE? :smile:thx
 
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  • #2
just draw and identify isosceles triangles.
You will get 40 degrees
 
  • #3
i did what you said, but angle ABE was 70*
 
  • #4
ABE=40 degress.
I think I have already posted it
 
  • #5
The solution:
The symbol of degree is omitted.

AD=BC (given)
BE=DC (given)
angleACD=180-angleBAC-angleADC (angle sum of triangle)
=180-35-110
=35
Because angleACD=angleBAC
Therefore DA=DC (sides opp. eq. angle)
angleCDB=angleACD+angleCAD (ext. angle of triangle)
=35+35
=70
DA=DC
DC=BC
angleCBD=angleCDB (base angles, isos. triangle)
=70
angleDCB=180-angleCBD-angleCDB (angle sum of triangle)
=180-70-70
=40
DC=BC
BE=BC
angleCEB=angleECB (base angles, isos. triangle)
=angleACD+angleDCB
=35+40
=75
angleABE+angleBAC=angleCEB (ext. angle of triangle)
angleABE+35=75
angleABE=40
 
Last edited:

FAQ: What is the size of angle ABE?

What is an angle?

An angle is a geometric figure formed by two rays with a common endpoint, also known as a vertex.

How is the size of an angle measured?

The size of an angle is measured in degrees (°) using a protractor. The protractor is placed on the angle with the vertex at the center and the baseline along one ray. The degree measure where the second ray intersects the protractor is the size of the angle.

What is the unit for measuring angles?

The unit for measuring angles is degrees (°). This is the most commonly used unit, but angles can also be measured in radians, gradians, and other units.

What does angle ABE refer to?

Angle ABE refers to the angle formed by the two rays AB and BE, with the vertex at point B.

Can angle ABE have a negative size?

No, angles cannot have a negative size. They are always measured in a positive direction, counterclockwise from the baseline.

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