Study Guide: Obtuse Angle

Definition:

An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees.

Example:

Let's consider an angle that measures 120 degrees. This angle is wider than a right angle (90 degrees) but less than a straight angle (180 degrees), so it is an obtuse angle.

Identification:

To identify an obtuse angle, look for an angle that appears wider than a right angle, but not a full rotation (which would be a straight angle).

Properties:

An obtuse angle has a measure greater than 90 degrees.
It is always less than 180 degrees.
The sum of the angles in a triangle is always 180 degrees, so a triangle can have at most one obtuse angle.

Practice Problems:

1. Identify the obtuse angles in the following figures:

2. Calculate the measure of an obtuse angle in a triangle when the other two angles are given as 45 degrees and 60 degrees.

Real-Life Application:

Obtuse angles can be found in various real-life situations, such as the opening angle of a wide V-shaped road junction or the angle between the minute and hour hand on a clock when it is between 9:00 and 12:00.

Remember, practice is key to mastering the concept of obtuse angles. Try to identify and calculate obtuse angles in different shapes and scenarios to strengthen your understanding.Now, let's solve the practice problem:

Practice Problem 1:

Identify the obtuse angles in the following figures:

Figure 1: <ABC = 70 degrees
Figure 2: <LMN = 120 degrees
Figure 3: <PQR = 150 degrees

Practice Problem 2:

Calculate the measure of an obtuse angle in a triangle when the other two angles are given as 45 degrees and 60 degrees.

Let's solve it step by step:

Step 1: Add the given angles to find the total angle measure of the triangle:

45° + 60° + <ABC = 180°

Step 2: Subtract the sum of the given angles from 180 degrees to find the measure of the obtuse angle:

<ABC = 180° - (45° + 60°)

<ABC = 180° - 105°

<ABC = 75°

◂Math Worksheets and Study Guides Eighth Grade. Collecting and describing data

Study Guide

Collecting and describing data

Worksheet/Answer key

Collecting and describing data

Worksheet/Answer key

Collecting and describing data

Worksheet/Answer key

Collecting and describing data

The resources above cover the following skills:

Data Analysis and Probability (NCTM)

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.

Select and use appropriate statistical methods to analyze data.

Find, use, and interpret measures of center and spread, including mean and interquartile range.

Develop and evaluate inferences and predictions that are based on data.

Use conjectures to formulate new questions and plan new studies to answer them.

Grade 8 Curriculum Focal Points (NCTM)

Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets

Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets, and they organize and display data to pose and answer questions. They compare the information provided by the mean and the median and investigate the different effects that changes in data values have on these measures of center. They understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center. Students select the mean or the median as the appropriate measure of center for a given purpose.

Connections to the Grade 8 Focal Points (NCTM)

Data Analysis: Building on their work in previous grades to organize and display data to pose and answer questions, students now see numerical data as an aggregate, which they can often summarize with one or several numbers. In addition to the median, students determine the 25th and 75th percentiles (1st and 3rd quartiles) to obtain information about the spread of data. They may use box-and-whisker plots to convey this information. Students make scatterplots to display bivariate data, and they informally estimate lines of best fit to make and test conjectures.