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Chapter 2: Problem 2

What is the supplement of a \(70^{\circ}\) angle? (GRAPH CANT COPY)

Short Answer

Expert verified
The supplement of a \(70^{\circ}\) angle is \(110^{\circ}\).

Step by step solution

01

Identify the Known Angle

The known angle is \(70^{\circ}\)
02

Find the Supplement

To find the supplement, subtract the given angle from \(180^{\circ}\). That is, \(180^{\circ} - 70^{\circ}\)
03

Calculate the Supplement

Subtracting \(70^{\circ}\) from \(180^{\circ}\) equals \(110^{\circ}\). So the supplement of a \(70^{\circ}\) angle is \(110^{\circ}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Angle Subtraction
In the realm of geometry, angle subtraction is a basic concept but extremely pivotal for problem-solving. When asked to find the supplement of an angle, you're actually tasked with using this concept. So, what does it mean? Quite simply, you subtract the given angle from a total that represents a complete half-turn, which is
  • For supplementary angles: By definition, supplementary angles add up to \(180^{\circ}\).
When encountering exercises like these, remember:
  • Carefully identify the angle you need to subtract.
  • Write down the expression required for subtraction, \(180^{\circ} - \text{given angle}\).
  • Calculate the result accurately.
Mastering angle subtraction can make these types of geometry problems a breeze even if they initially seem challenging.
Geometry Problem Solving
Geometry involves many fascinating challenges, one of which is problem-solving using supplementary angles. Identifying the type of geometric problem at hand is crucial:
  • Ensure you're dealing with supplementary angles. They always sum up to \(180^{\circ}\).
  • Use logic to approach these problems. For example, if you're given a problem like finding a supplement, look for hints about the known angle.
Problem solving means structuring your solution in steps:
  • Start by identifying known facts鈥攍ike the angle given.
  • Act on these facts鈥攑erform calculations like angle subtraction.
  • Double-check your solution to ensure it's logical and accurate.
Always double-check your calculations. Geometry problems usually have a clear logical path, so if your solution doesn鈥檛 seem to add up, rethink your steps.
Basic Angle Concepts
Before diving into specific problems, it's wise to reflect on basic angle concepts. Understanding these fundamentals aids in grasping more complex problems.
  • The full rotation of a circle is \(360^{\circ}\).
  • A straight line or half-turn represents \(180^{\circ}\).
  • Supplementary angles are any two angles that add up to \(180^{\circ}\).
  • Complementary angles, on the other hand, add up to \(90^{\circ}\).
Understanding these core principles makes identifying and solving geometry problems more manageable. Knowing the difference between complementary and supplementary angles is imperative.Often, students mix up these basic angle types, but remembering that the term 'supplementary' is associated with the term 'straight line'鈥攂oth indicating \(180^{\circ}\)鈥攃an help guide and refine your understanding. Knowing these concepts forms the foundation for solving complex geometry exercises easily.

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Most popular questions from this chapter

On a graph, point \(A\) is at \((0,4)\). Point \(A\) is then rotated \(90^{\circ}\) clockwise about the origin to point \(A^{\prime}\). What are the coordinates of A'?

Debbie has drawn distinct rays \(\overrightarrow{\mathrm{BA}}, \overrightarrow{\mathrm{BC}}, \overrightarrow{\mathrm{BD}}, \overrightarrow{\mathrm{BE}},\) and \(\overrightarrow{\mathrm{BF}}\) on a piece of paper, with \(\angle \mathrm{ABC}\) being a straight angle. a What is the minimum number of pairs of complementary angles that she could have drawn? b What is the maximum number of pairs of complementary angles that she could have drawn? c What is the minimum number of pairs of supplementary angles that she could have drawn? d What is the maximum number of pairs of supplementary angles that she could have drawn?

Given: \(\angle \mathrm{PQR}\) supp. \(\angle \mathrm{QRS},\) LQRS supp. \(\angle \mathrm{TWX}\) $$\angle \mathrm{PQR}=(5 \mathrm{x}-48)^{\circ}, \angle \mathrm{TWX}=(2 \mathrm{x}+30)^{\circ}$$ Find: \(\mathrm{m} \angle \mathrm{QRS}\)

Given: \(\overrightarrow{\mathrm{SV}}\) bisects \(\angle \mathrm{RST}\). Conclusion: \(\angle \mathrm{RSV} \cong \angle \mathrm{TSV}\)

Five times the complement of an angle less twice the angle's supplement is \(40^{\circ} .\) Find the measure of the supplement.
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