Solving Geometry Angles Problems

By Author: Pierce Brosnan
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Introduction solving geometry angles problems:

Geometry is the most important branch in math. It involves study of shapes. It also includes plane geometry, solid geometry, and spherical geometry. Plane geometry involves line segments, circles and triangles. Solid geometry includes planes, solid figures, and geometric shapes. Spherical geometry includes all spherical shapes. Line segment is the basic in geometry. There are many 2D, 3D shapes.2D shapes are rectangle, square, rhombus etc. 3D sahpes are Cube, Cuboid and pyramid and so on. Basic types of angles are complementary angles and supplementary angles and corresponding angles, vertical angles.

Basic Geometric Properties used in solving angles problems

Some important theorems used in solving geometry angles problems :

The sum of the complementary angles is always 90 degree.
The sum of the supplementary angles is always 180 degree.
When two parallel lines crossed by the transversal the corresponding angles are formed. Those angles are equal in measure.
When two lines are intersecting then the vertical angles are always ...
... equal.
In a parallelogram the sum of the adjacent angles are 180 degree. And the opposite angles are equal in measure.

Solving example of geometry angles problems

Solving geometry angles problems using the above properties :

Pro 1. One of the given angles is 50. Solve its complementary angle.

Solution:A sum of complementary angle is 90 degree.

Given angle is 50

So the another angle = 90-50

So the next angle = 40

Pro 2. One of the given angles is 120. Solve its supplementary angle.

Solution: A Sum of supplementary angles is 180 degrees

Given angle is 120 degrees.

So, the unknown angle = 180-120.

So,the unknown angle = 60 degrees.

Pro 3. The angle given is 180.Solve its corresponding angles.

Solution:Corresponding angles are equal

So, the answer is 180

Pro 4. A figure has an angle of 45 degrees. Solve its vertically opposite angle.

Solution:Vertically opposite angles are equal.

So, the answer is 45 degrees.

Pro 5. One of the two angles of the triangle is 55 and 120 degree. Solve the measure of third angle

Solution:Sum of angles = 180 degrees.

So, the third angle = 180 – (55 + 120)

= 180 - 175

= 5 degrees

So, third angle is 5 degrees.

Pro 6. If one angle of the parallelogram is 60 degree. Solve the other three angles.

Solution:A sum of the angles in a parallelogram is 360 degree.

In a parallelogram adjacent angles are supplementary and opposite angles are equal.

Therefore, opposite angle of 60 degree is also 60 degree.

And the adjacent angle of 60 degree is 180 - 60 =120 degree.

Here, other three angles are 60 degree and 120 degree, 120 degree.

Comprehend more on about Classifying Angles and its Circumstances. Between, if you have problem on these topics What are Alternate Interior Angles Please share your views here by commenting.