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Chapter 9: Problem 33

Find the measure of a supplement of each angle. $$ 85^{\circ} $$

Short Answer

Expert verified
The supplement of 85掳 is 95掳.

Step by step solution

01

Understand the concept of supplementary angles

Supplementary angles are two angles whose measures add up to 180掳.
02

Identify the given angle

The angle provided in the problem is 85掳.
03

Set up the equation

To find the measure of the supplement of the given angle, set up the equation: 85掳 + x = 180掳.
04

Solve for x

Subtract 85掳 from both sides of the equation to find the measure of the supplementary angle: x = 180掳 - 85掳.
05

Calculate the result

Perform the subtraction: x = 95掳.

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Key Concepts

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

mathematics
Mathematics is a broad subject that deals with numbers, formulas, shapes, and patterns. It is divided into various disciplines such as arithmetic, algebra, geometry, and calculus. In this exercise, we focus on geometry, more specifically the concept of supplementary angles. Mathematics helps us understand the world around us, offering tools for analysis and problem-solving. Whether you're measuring angles in a triangle or calculating the area of a circle, mathematics provides the foundation.
angle measurement
Angle measurement is a key concept in geometry. Angles are formed by two rays (or line segments) that share a common endpoint. The size of an angle is measured in degrees (掳), ranging from 0掳 to 360掳.
There are different types of angles based on their measurements, including:
  • Acute angles: less than 90掳
  • Right angles: exactly 90掳
  • Obtuse angles: between 90掳 and 180掳
  • Straight angles: exactly 180掳
For an angle measuring 85掳, its supplementary angle will be such that their measures add up to 180掳. This understanding helps you calculate unknown angles.
geometry basics
Geometry is a branch of mathematics that studies the sizes, shapes, properties, and dimensions of objects and spaces. One essential concept in geometry is the measurement of angles and their relationships.
For example, supplementary angles are two angles whose measures add up to 180掳.
  • If angle A measures 85掳, the supplement of angle A will measure 180掳 - 85掳 = 95掳.
Understanding this basic principle allows you to solve problems like identifying the measures of various angles and their relationships. Geometry not only helps in academic settings but is also practical in real-world applications like architecture and engineering.

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