Angles

Angles: An angle is  formed by the union of two rays with the common origin. The origin is called vertex and the two rays form two sides of the angle. An angle is denoted by sign <.

Transversal is a line which cuts two or more coplanar (in the same plane) lines in distinct points.
Let AB and CD be two parallel lines and EF be the transversal (as shown in the figure below).

As we can see above, transversal EF cuts AB and CD as a result of various angles are formed (angle a,b,c,d,e,f,g and h as shown in the diagram above).

We will try to understand various properties of angles:
Alternate interior angles
The following pairs are alternate interior angles:
<c and <f
<d and <e
In case lines AB and CD are parallel, the alternate interior angles are equal to each other.
Alternate exterior angles
The following pairs are alternate exterior angles:
<a and <h
<b and <g
In case lines AB and CD are parallel, the alternate exterior angles are equal to each other.
Vertically opposite angles
<a = <d; <b = <c; <e = <h; <f= <g
Corresponding angles
<a and <e
<c and <g
<b and <f
<d and <h

 

Consecutive interior angles

The following pairs are consecutive interior angles:
<c and <e
<d and <f
In case lines AB and CD are parallel, <c + <e =180° and <d + <f = 180°.

Complementary angles
<a and <b are complementary to each other as <a +<b =90° since the points A, O and B constitute a right angle with O as its vertex.

 

Supplementary angles

<a and <b are supplementary to each other as <a +<b =180° since the points A, O and B lie on one straight line.

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