Solved Examples on Complementary Angles
Example 1: Are 46° and 44° complementary angles? Give reason.
Solution:
Given two angles i.e., 46° and 44° .
We know that two angles are said to be complementary if their sum is 90°.
Since 46° + 44° = 90°
Thus, 46° and 44° are complementary angles.
Example 2: Find the complement of 61°.
Solution:
We know that the complement of an angle measuring x° = (90 – x)°.
Here, x° = 61°
Complement of 61° = (90 – 61)° = 29°
Thus, the complement of 61° = 29°
Example 3: Find the value of sec 37° cosec 53° – tan 37° cot 53°.
Solution:
sec 37° cosec 53° – tan 53° cot 37°
We know that cot θ = tan (90° – θ) and cosec θ = sec (90° – θ)
cot 53° = tan (90° – 53°) and cosec 53° = sec (90° – 53°)
cot 53° = tan 37° and cosec 53° = sec 37°
On substituting the values, we get
sec 37° sec 37° – tan 37° tan 37°
= sec237° – tan237° = 1
Hence, sec 37° cosec 53° – tan 37° cot 53° = 1
Example 4: Find the value of x, if (x + 3)° and (x – 5)° form complementary angles.
Solution:
We know that two angles are said to be complementary if their sum is 90°.
So, (x + 3)° + (x – 5)° = 90°
(x + x + 3 – 5)° = 90°
(2x – 2)° = 90°
2(x – 1)° = 90°
(x – 1)° = 45°
x = (45 + 1)°
x = 46°
Hence, the value of x is = 46°.
Example 5: If sin 2A = cos (A – 27°), where A is an acute angle, find A.
Solution:
sin 2A = cos (A – 27°)
We know that sin θ = cos (90° – θ)
sin 2A = cos (90° – 2A)
On substituting the value, we get
cos (90° – 2A) = cos (A – 27°)
90° – 2A = A – 27°
90° + 27° = 3A
A=\frac{117^{\circ}}{3}
A = 39°
Complementary Angles
Two acute angles are said to be complementary angles if the sum of the angles equals 90° i.e., complementary angles are those angles whose sum adds up to 90°. In other words, we can say that the sum of complementary angles is 90°.
Complementary Angles are not just a term that is used in geometry as this also has some real-life applications. One such example is slicing a rectangular-shaped bread along the diagonal. We will get two right triangles, each with a pair of complementary angles. In this article, we will be learning about the definition of complementary angles, types of complementary angles, properties, and how to find the complement of an angle.
Table of Content
- What are Complementary Angles?
- Complementary Angles Examples
- Types of Complementary Angles
- Properties of Complementary Angles
- Complementary Angle Theorem
- Complementary Angles vs Supplementary Angles