Two angles are supplementary. The first angle measures $60^{\circ}$. What's the measurement of the second angle?
A) $180^{\circ}$
B) $30^{\circ}$
C) $120^{\circ}$
D) $90^{\circ}$
Answer (2)
Define supplementary angles: Two angles are supplementary if their sum is 18 0 ∘ .
Set up the equation: If the first angle is 6 0 ∘ and the second angle is b , then 6 0 ∘ + b = 18 0 ∘ .
Solve for b : Subtract 6 0 ∘ from both sides to find b = 18 0 ∘ − 6 0 ∘ .
State the final answer: The second angle measures 12 0 ∘ .
Explanation
Problem Analysis Let's analyze the problem. We know that two angles are supplementary, which means their measures add up to 18 0 ∘ . We are given that the first angle measures 6 0 ∘ , and we need to find the measure of the second angle.
Setting up the equation Let the first angle be a and the second angle be b . We know that supplementary angles add up to 18 0 ∘ , so we can write the equation: a + b = 18 0 ∘ We are given that a = 6 0 ∘ . Substituting this value into the equation, we get: 6 0 ∘ + b = 18 0 ∘
Solving for the second angle To solve for b , we subtract 6 0 ∘ from both sides of the equation: b = 18 0 ∘ − 6 0 ∘ b = 12 0 ∘
Final Answer Therefore, the measurement of the second angle is 12 0 ∘ .
Examples
Supplementary angles are commonly used in architecture and engineering to ensure structural stability. For example, when designing a bridge, engineers use supplementary angles to calculate the correct angles for support beams, ensuring that the bridge can withstand the intended load. Similarly, in construction, carpenters use supplementary angles when cutting wood to create precise corners and joints, ensuring that the structure is sound and aesthetically pleasing. Understanding supplementary angles helps in creating balanced and stable designs.
The second angle is calculated to be 12 0 ∘ , since supplementary angles add up to 18 0 ∘ . Therefore, the answer is C) 12 0 ∘ .
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