Question

How do you find the complement and supplement of $ {130^ \circ } $ ?

Answer 1

Hint: The two angles are called complementary if their sum comes out to be a right angle. Right angle is called $ {90^ \circ } $ in geometrical terms . Similarly for the definition of supplementary angles we write that for two angles angles to be supplementary in nature, the angles when added should be equal to a straight angle. The straight angle is also called as $ {180^ \circ } $ geometrically. Thus to find the complementary angle of a particular given angle we subtract the given angle from the measure of a right angle and similarly for supplementary angle we subtract the given angle from the measure of a straight angle. In this case the measure of the given angle is more than the measure of a right angle so the complementary angle will come out to be in the negative angle.

Complete step by step solution:
The two angles when added form a right angle then those angles are called complementary angles. We are given the value of our angle as:
 $ {130^ \circ } $ For finding the value of its complement we subtract the angle from $ {90^ \circ } $ . Thus the complementary angle will be
 $ = {90^{^ \circ }} - {130^ \circ } $
 $ = - {40^ \circ } $
Thus the complementary angle of $ {130^ \circ } $ is $ - {40^ \circ } $
The similar procedure goes for a supplementary angle whose sum of two angles should be a straight angle. The supplementary angle of $ {130^ \circ } $ will be
\[ = {180^ \circ } - {130^{^ \circ }}\]
 $ = {50^ \circ } $ .
Thus the supplementary angle of $ {130^ \circ } $ is $ {50^ \circ } $

Note: Remember that a linear pair of angles in geometry always has the sum equal to the straight angle which is $ {180^ \circ } $ and they are supplementary to each other.