Two angles are supplementary. The first angle measures $40^{\circ}$. What's the measurement of the second angle?
A) $60^{\circ}$
B) $140^{\circ}$
C) $120^\circ$
D) $50^{\circ}$
Answer (2)
Recognize that supplementary angles sum to 18 0 ∘ .
Substitute the given angle ( 4 0 ∘ ) into the supplementary angle equation.
Solve for the unknown angle by subtracting 4 0 ∘ from 18 0 ∘ .
Conclude that the second angle measures 14 0 ∘ .
Explanation
Problem Analysis We are given that two angles are supplementary, meaning their sum is 18 0 ∘ . The first angle measures 4 0 ∘ . We need to find the measure of the second angle.
Define variables and state equations Let the first angle be a and the second angle be b . We know that a = 4 0 ∘ and a + b = 18 0 ∘ .
Substitution Substitute the value of a into the equation: 4 0 ∘ + b = 18 0 ∘ .
Isolate b Solve for b by subtracting 4 0 ∘ from both sides of the equation: b = 18 0 ∘ − 4 0 ∘ .
Calculate the result Calculate the value of b : b = 14 0 ∘ . Therefore, the measurement of the second angle is 14 0 ∘ .
Examples
Understanding supplementary angles is useful in architecture and design. For example, when designing a roof, knowing that the angles must be supplementary helps ensure the roof fits correctly and provides the necessary support. In art, supplementary angles can be used to create balanced and visually appealing compositions. Imagine creating a mosaic where the angles of the tiles need to fit together perfectly; understanding supplementary angles is crucial for achieving a seamless design.
The second angle is 14 0 ∘ since supplementary angles add up to 18 0 ∘ . The equation used is 18 0 ∘ − 4 0 ∘ = 14 0 ∘ . Therefore, the correct choice is B) 14 0 ∘ .
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