Difference of angles in a triangle

Click For Summary

Discussion Overview

The discussion revolves around calculating the difference in degrees between the measures of the two smallest angles in triangle ABC, given specific angle measures and the use of angle bisectors. The scope includes mathematical reasoning and problem-solving without reliance on software tools like Geogebra.

Discussion Character

  • Mathematical reasoning, Homework-related

Main Points Raised

  • One participant states the known angles BDE and CED are 24 and 18 degrees, respectively, and provides the measure of angle CAB as 96 degrees.
  • Another participant recalls that the angles in a triangle sum to 180 degrees and suggests using inspection to determine the angles in the triangle.
  • A participant asks how to calculate angle ABC specifically.
  • Multiple participants express uncertainty about solving the problem without Geogebra and inquire about the application of the angle bisector theorem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to solve the problem without Geogebra, and there are multiple inquiries about the use of the angle bisector theorem, indicating uncertainty and a lack of agreement on the approach.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about angle measures and the reliance on visual aids or external resources for problem-solving.

maxkor
Messages
79
Reaction score
0
In a triangle ABC, let D and E be the intersections of the bisectors of the angles ABC and ACB with the sides AC and AB, respectively. Knowing that the measures in degrees of the angles BDE and CED are equal to 24 and 18, respectively, calculate the difference in degrees between the measures of the two smallest angles of the triangle. CAB angle = 96 degrees.

I checked with Geogebra:
Geogebra online(7).png

But how to solve this problem without Geogebra?
 
Mathematics news on Phys.org
Recalling that plane Euclidean triangle angles add up to 180 degrees, opposite angles in intersecting lines are equal and angle bisectors split angles in half, we can use inspection to determine all the angles in the diagram.

As an example, by inspection, triangle DEI has two angles shown so we can compute the missing angle EID as 180-24-18 = 138 degrees.
 
  • Like
Likes   Reactions: Greg Bernhardt
so how to calculate for example angle ABC?
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
1
Views
2K