 Hi and welcome to the session. Today we will learn about pairs of angles. But before moving on to the topic of pairs of angles, let us see how an angle is formed. And for that let us see what is a line segment, a line array. A line segment has two end points, say p and q. So here p, q is a line segment. Now if we have a line segment ab and we extend the two end points of the line segment ab in either direction endlessly then it will become a line. So here ab is a line. Thus a line has no end points. Now a line has one end point, say o that is the starting point and here we have a point x. So here o x is the way. Now let's see how an angle is formed. An angle is formed when two lines or two line segments meet. So here this is angle abc. Now the measure of an angle, say angle abc is simply written as angle abc. An acute angle is an angle which is less than 90 degrees. A right angle is an angle which is equal to 90 degrees. An active angle is an angle which is greater than 90 degrees but less than 180 degrees. Now let's see what are complementary angles. Here suppose we have two angles angle abc and angle eqr where angle abc is equal to 20 degrees and angle pqr is equal to 70 degrees. Now if we add the measure of these two angles then 20 degrees plus 70 degrees will be equal to 90 degrees. So here the sum of two angles is equal to 90 degrees. That means these two angles are complementary angles. So we can say that two complementary angles are those whose measures add up to 90 degrees. Two angles are complement of each other. So here angle abc is the complement of angle pqr and angle pqr is the complement of angle abc. Now let's see what are supplementary angles. Here we have angle abc equal to 53 degrees and angle pqr equal to 127 degrees. Now some of the measures of these two angles will be 53 degrees plus 127 degrees which is equal to 180 degrees. So as the sum of these two angles is 180 degrees that means we can say that these two angles are supplementary angles. Thus we have two supplementary angles are those whose measures add up to 180 degrees. And the two angles which are supplementary angles are supplement of each other. So we have they are supplement of each other. That means here angle abc is the supplement of angle pqr and angle pqr is the supplement of angle abc. Let's move on to adjacent angles. Adjacent angles are those angles which have a common vertex having common r on the either side. Also the two adjacent angles interior point cbd are adjacent angles as they have a common vertex b they have a common arm cb. The non-common arms ab and bd are on the either side of the common arm cb and they have no common interior points. Next we have a linear pair. A linear pair is a pair adjacent angles. So here angle abc say angle 1 and angle cbd say angle 2 form a linear pair because they are adjacent angles and they are non-common sides. That is the a and bd are opposite rings and here angle 1 plus angle 2 will be equal to 180 degrees. Thus we have that angles in a linear supplementary angles will form a linear pair if we place them adjacent to each other. Now our last topic is vertically opposite angles. Here we have two lines line p and line q intersecting each other at point angle 2, angle 3 and which are these two pairs. Angle 1 and angle 3 form a pair of vertically opposite angles form a pair of vertically opposite angles. Now if intersect so here angle 1 is equal to angle 3 and angle 2 is equal to angle 4 as the lines p and q intersect each other. Let's take an example now and the measure of this angle and we need to find out the measure of other angles that is the value of x, y and z. Let us name these angles as angle 1, angle 2, angle 3 and angle 1 plus angle 4 will be equal to 180 degrees as they form a linear pair. The values we will get angle 1 that is 125 degrees plus angle 4 that is y is equal to 180 degrees. So the value of y will be equal to 180 degrees minus 125 degrees which will be equal to 55 degrees. Thus here angle 4 that is y is equal to 55 degrees. Now angle 1 will be equal to angle 3 and angle 2 will be equal to angle 4 as they form pairs of vertically opposite angles. If angle 2 is equal to 125 degrees that means angle 3 which is equal to angle 1 will be equal to 125 degrees. That means the value of x is equal to 125 degrees. Is equal to angle 4 and angle 4 is equal to 55 degrees that means angle 2 will be equal to 55 degrees. This implies the value of z is equal to 55 degrees. With this, we finish this session. Hope you must have understood all the concepts. Goodbye, take care and have a nice day.