Problem 211 - Elementary Algebra

Question

In the following exercises, solve using triangle properties. The measures of two angles of a triangle are 26 and 98 degrees. Find the measure of the third angle.

Step-by-Step Solution

Answer

The measure of the third angle is 56 degrees.

Step 1 - Recall the Triangle Angle Sum Property

Recall that the sum of the angles in any triangle is always 180 degrees. This is known as the Triangle Angle Sum Property.

Step 2 - Add Given Angles

Add the measures of the two given angles: 26 + 98 = 124 degrees.

Step 3 - Subtract from 180 Degrees

Subtract the sum of the given angles from 180 degrees to find the measure of the third angle: 180 - 124 = 56 degrees.

Key Concepts

Triangle Angle Sum Property

Triangles are fascinating shapes in geometry. One key property of them is that the sum of all interior angles always equals 180 degrees. No matter if the triangle is equilateral, isosceles, or scalene, when you add up the three angles, you will always get 180 degrees. This is known as the Triangle Angle Sum Property. Understanding this property is crucial because it is the foundation for solving many problems involving triangles.
For example, if you know two of the angles in a triangle, you can easily find the third angle using this property.
This property simplifies the process of angle calculations, making it a fundamental tool in geometry.

Angle Measurement

When working with triangles, it is important to be able to measure angles accurately. Angles are typically measured in degrees, and there are useful tools like protractors that help with this.
In our example, the measures of two angles are provided as 26 degrees and 98 degrees. These values help us proceed with calculations to determine the third angle. Accurate measurements ensure our calculations are correct and reliable. It is also important to note that the notation for degrees is a small circle (°) placed after the number, so 26 degrees is written as 26°.
Being comfortable with measuring and working with angles is a key skill in geometry.

Triangle Angles Calculation

Once we know the Triangle Angle Sum Property and have precise angle measurements, we can easily find unknown angles in a triangle. Here’s a simple method to follow:

• Add the given angles together.
• Subtract this sum from 180 degrees.

In our example with angle measures of 26 degrees and 98 degrees, we add them:
26 + 98 = 124 degrees.
Next, we subtract this total from 180 degrees:
180 - 124 = 56 degrees.
Thus, the measure of the third angle is 56 degrees.
With this method, you can solve many problems related to triangle angles quickly and effectively.