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How to Find a Indicated Angle Measures

How to Find Indicated Angle Measures?

The angle concept is one of the very important concepts involved in geometry. 
Hence the area of trigonometry subject is mainly based on the measurements of angles. 
In order to find the measurements of indicated angles, the basic concepts of sum, equality, and the differences of angles are needed to be well known. 
There are mainly two measurement units for angles, of which degree is the most familiar. 
A circle is exactly divided into equal 360 degrees. After this, each degree is subdivided into 60 minutes. 

For example, eight and a half degree means eight degrees and 30 minutes. 
For finding the measurement of the indicated angle of several geometries, it is required to know well about those geometry’s angle properties as well as their other geometrical properties.

There are mainly Three Types of Angles Namely

i) Acute angle when it is less than 90 degrees 
ii) Right angle when it is equal to 90 degrees and 
iii) Obtuse angle which is greater than 90 degrees. 
Also, complementary angles are two angles whose sum adds up to 90 degrees and supplementary angles are two angles whose sum will be 180 degrees.
Now we will look at the methods to find the indicated angle measure of various geometries like triangle, polygon, parallelogram, etc. 
In order to find the left out angle of a triangle, we can use the formula “the sum of three angles of a triangle will always be 180 degrees”. 
Hence if we subtract the given two angles with 180, the remaining value gives the indicated angle measurement.

In general for a polygon of ‘n’ sides, the sum of interior angles would be (n-2) multiplied by 180 degrees. 
The ‘n’ decides the name of the geometry such as quadrilateral if a polygon has four sides, pentagon if it has five sides, etc. 
Below example would give a glance of finding the indicated angle measurement. 
If the top left side and bottom right side of the parallelogram is 3x, then how will you find the other two measures?

When we draw a diagonal in the parallelogram, then we will get two equal triangles. 
We know well that, total angles of triangle ads up to 180 degrees and hence obviously it will be 360 degrees for a parallelogram. 
So now adding all the four angles of 3x, 3x, y and y, where y is the other side, we will get sum of 6x and 2y equaling 360. 
Now moving that 6x to the right, we will get 2y equaling 360 - 6x. 
Finally, we will get y as 180 - 3x. 
Thus, by knowing the value of x, we can get the value of y.