The ratio of the measure of the supplement of an angle to that of a complement of the angle is 3:1. Find the measure of the supplement.
Answers
Step-by-step explanation:
a+b=180___1
a-b=90__2
1/2 =3/1
a+b=180÷a-b=90=3÷1
a/b=3
a =3b
3b+b=180
4b=180
b=45
a+45=180
a=180-45
a=135
a+b=180
45+135=180
a-b=90
135-45=90
The require answer is 45°
supplement angel : Supplementary angles are those angles that add up to 180 degrees. For example, an angle of 130° and an angle of 50° are complementary angles because the sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees. Two supplementary angles, when joined together, form a straight line and a right angle.
But it should be noted that two complementary angles need not be adjacent. Thus, any two angles can be supplementary angles if their sum is equal to 180°.
Geometry is one of the important branches of mathematics that deals with the study of different shapes. Begins the study of lines and angles. A straight line is a line without curves and is defined as the shortest distance between two points. An angle is formed when a line meets a point.
complement angle : When the sum of two angles is 90°, then the angles are known as complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as supplementary angles. Here we say that these two angles are complementary.
let angle be x
supplement will be 180-x
complement will be 90-x
Therefore the given ratio is 3:1
180-x/(90-x)=3/1
180-x=3(90-x)
180-x=270-3x
3x -x =270 -180
2x=90
x = 45°
x=45°.
Hence the require answer is 45°.
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