Difference of angles in a triangle

In summary, the conversation discusses a problem involving a triangle ABC and its bisectors, D and E. The measures of angles BDE and CED are given, and the task is to find the difference in degrees between the two smallest angles of the triangle. It is suggested to use the properties of intersecting lines and angle bisectors, as well as the fact that triangle angles add up to 180 degrees, to solve the problem without relying on Geogebra. The Angle Bisector Theorem is mentioned as a potential tool for solving the problem.
  • #1
maxkor
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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?
 
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  • #2
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.
 
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Likes Greg Bernhardt
  • #3
so how to calculate for example angle ABC?
 

1. What is the difference of angles in a triangle?

The difference of angles in a triangle refers to the difference between the largest angle and the smallest angle in the triangle. It is also known as the angle sum property, which states that the sum of all angles in a triangle is always equal to 180 degrees.

2. How can I find the difference of angles in a triangle?

To find the difference of angles in a triangle, you can subtract the smallest angle from the largest angle. For example, if the largest angle is 90 degrees and the smallest angle is 30 degrees, the difference would be 60 degrees.

3. Is the difference of angles in a triangle always the same?

No, the difference of angles in a triangle can vary depending on the size and shape of the triangle. However, the sum of all angles in a triangle will always be 180 degrees.

4. Why is the difference of angles in a triangle important?

The difference of angles in a triangle is important because it helps us identify the type of triangle. For example, if the difference is 0 degrees, then the triangle is equilateral. If the difference is 90 degrees, then the triangle is right-angled. It also helps us understand the relationship between the angles in a triangle.

5. Can the difference of angles in a triangle be negative?

No, the difference of angles in a triangle cannot be negative. It is always measured as a positive value, as it represents the difference between two angles. If the difference is negative, it means that the angles were not measured correctly or that the triangle is not a valid triangle.

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