Question

The sum of the measures of the angles of any triangle is 180 degrees . In a certain triangle, the largest angle measures 55degrees less than twice the medium angle, and the smallest angle measures 25 degrees less than the medium angle. Find the measures of each of the three angles.

Answer 1

Each of the three angles of the triangles whose sum of angles is 180 degree measures 75°, 65°, and 40°

What is meant by measurement of angles?

An easy geometric instrument like a protractor is used to measure angles. A protractor is employed more frequently than a compass. Angle measurement is important for determining the precise angle. In geometry, there are several sorts of angles that we face in our daily lives, and we may measure angles using these tools.

Basic geometric instruments like a protractor and a compass are used to measure angles. These instruments aid in determining an angle's precise measurement. A protractor aids in producing an accurate angle measurement, while a compass aids in creating the angle. Angles can be measured in three different ways: in degrees, radians, and revolutions.

Here, we have

Let the largest angle be x degrees, the median y, and the smallest z.

x = 2y - 55

z = y - 25

x + y + z = 180

Substituting for x in the last equation:

2y - 55 + y + z = 180

3y + z = 235  

From the second equation:

- y + z = -25     Subtract this from the last equation:

4y = 260

y = 65 degrees

z = 65 - 25 = 40 degrees.

and x = 180 - 65 - 40 = 75 degrees.

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