Find the complement of an angle that measures $78^{\circ}$.
A) $22^{\circ}$
B) $12^{\circ}$
C) $42^{\circ}$
D) $102^{\circ}$
Answer (1)
The problem asks to find the complement of a 7 8 ∘ angle.
Complementary angles add up to 9 0 ∘ .
Subtract the given angle from 9 0 ∘ to find its complement: 9 0 ∘ − 7 8 ∘ = 1 2 ∘ .
The complement of the angle is 1 2 ∘ .
Explanation
Understanding Complementary Angles We are given an angle that measures 7 8 ∘ , and we want to find its complement. Two angles are complementary if their measures add up to 9 0 ∘ .
Calculating the Complement To find the complement of the given angle, we subtract its measure from 9 0 ∘ . So, we need to calculate 9 0 ∘ − 7 8 ∘ .
Finding the Answer The calculation is as follows: 9 0 ∘ − 7 8 ∘ = 1 2 ∘ Therefore, the complement of a 7 8 ∘ angle is 1 2 ∘ .
Examples
In architecture, complementary angles are crucial for designing structures that require precise angles for stability and aesthetics. For example, when building a roof, the angles of the supporting beams must be complementary to ensure the roof sits correctly and can withstand external forces. If one angle is 7 8 ∘ , its complement ( 1 2 ∘ ) is needed to complete a right-angled support structure, ensuring the roof's stability and proper alignment.
