Basics of Geometry Angles
Types of angles Right Angle Obtuse Angle Acute Angle An angle greater than O but less than 90 An angle of 90 is called right angle An angle greater than 90Pbut less than 180 Reflex Angle Straight Angle An angle of 180is called a straight angle An angle greater than 90 but less than 360'is relex angle
Angles made by traversal 1.Corresponding angles When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles Example: <1 &<5 are corresponding angles ng Therefore <1-<5 as corresponding angles are equal
Angles made by traversal 2.Interior angles of traversal: If the transversal cuts across parallel lines (the usual case) then the interior angles are supplementary (add to 180 ). So in the figure points <3 or <4, the two interior angles shown always add to 180.
Angles made by traversal 3.Exterior angles of traversal: If the transversal cuts across parallel lines then exterior angles are supplementary (add to 180 ). So in the figure the two angles and <7 shown always add to 180 Similarly, 2 and <8 always add to 180 .
Angles made by traversal 4.Alternate interior angles When two lines are crossed by another line a pair of angles on the inner side of each of those two lines and on opposite sides of the transversal are called Alternate Interior Angles. Here <3 2 are alternate angles and are equal
Angles made by traversal 5.Alternate exterior angles: When two lines are crossed by another line a pair of angles on each of those two lines and on opposite sides of the transversal but outside those two lines are called Alternate Exterior Angles Here,1 8 as they are alternate exterior
Problem .Find the values of x and y from the given geometric figure.
Solution Since 57 and x are interior alternate angles, they are supposed to be equal. So, x=570. . 420 is an exterior angle and it's alternate exterior is supplementary angle of y. So, supplementary angle of y is 42. Therefore, y-180-42, that is y-138 .