Podcast
Questions and Answers
What is the relationship between the supplement and the complement of a given angle according to the problem?
What is the relationship between the supplement and the complement of a given angle according to the problem?
If x represents the measure of the unknown angle, how would the complement of the angle be expressed?
If x represents the measure of the unknown angle, how would the complement of the angle be expressed?
Given the relationship stated, how would you set up an equation to find the angle x?
Given the relationship stated, how would you set up an equation to find the angle x?
What is the next step after forming the equation from the angle relationships?
What is the next step after forming the equation from the angle relationships?
Signup and view all the answers
What are the measures of the angles if the angle x is found to be 44 degrees?
What are the measures of the angles if the angle x is found to be 44 degrees?
Signup and view all the answers
How can the accuracy of the determined angle values be verified?
How can the accuracy of the determined angle values be verified?
Signup and view all the answers
If x represents an angle of 30 degrees, what would be its complement?
If x represents an angle of 30 degrees, what would be its complement?
Signup and view all the answers
What does it mean if two angles are complementary?
What does it mean if two angles are complementary?
Signup and view all the answers
What is the relationship between two complementary angles?
What is the relationship between two complementary angles?
Signup and view all the answers
If one angle measures 16⁰ more than its complement, what equation can be set up to represent this relationship?
If one angle measures 16⁰ more than its complement, what equation can be set up to represent this relationship?
Signup and view all the answers
In a right triangle, if one angle is represented as x, which of these represents the measure of the other non-right angle assuming it is twice the first angle?
In a right triangle, if one angle is represented as x, which of these represents the measure of the other non-right angle assuming it is twice the first angle?
Signup and view all the answers
What would be the first step to find the measures of angles in a right triangle if one angle is twice the measure of another?
What would be the first step to find the measures of angles in a right triangle if one angle is twice the measure of another?
Signup and view all the answers
What is the value of x if the equation is set up as 90 + 3x = 180?
What is the value of x if the equation is set up as 90 + 3x = 180?
Signup and view all the answers
If complementary angles are represented as m∠1 and m∠2, which equation correctly expresses their relationship?
If complementary angles are represented as m∠1 and m∠2, which equation correctly expresses their relationship?
Signup and view all the answers
In a problem involving angles of a right triangle, if the right angle is 90⁰, which statement must be true?
In a problem involving angles of a right triangle, if the right angle is 90⁰, which statement must be true?
Signup and view all the answers
Given two complementary angles, if one angle is x, what is the expression for its complement?
Given two complementary angles, if one angle is x, what is the expression for its complement?
Signup and view all the answers
What is the value of $x$ in the equation $7x + 12 = 180$?
What is the value of $x$ in the equation $7x + 12 = 180$?
Signup and view all the answers
If one angle is represented as $6x + 12$, what is the relationship between this angle and the angle represented by $x$?
If one angle is represented as $6x + 12$, what is the relationship between this angle and the angle represented by $x$?
Signup and view all the answers
What is the sum of the measures of the angles if one angle is $24^ ext{o}$ and its supplement is $156^ ext{o}$?
What is the sum of the measures of the angles if one angle is $24^ ext{o}$ and its supplement is $156^ ext{o}$?
Signup and view all the answers
When $x = 24$, what is the measure of its supplement?
When $x = 24$, what is the measure of its supplement?
Signup and view all the answers
How is the second angle compared to the first angle in the triangle problem described?
How is the second angle compared to the first angle in the triangle problem described?
Signup and view all the answers
If the third angle of the triangle is $3^ ext{o}$ less than twice the first angle, what expression represents the third angle?
If the third angle of the triangle is $3^ ext{o}$ less than twice the first angle, what expression represents the third angle?
Signup and view all the answers
What is the equation used to express the relationship between the angles in the triangle problem?
What is the equation used to express the relationship between the angles in the triangle problem?
Signup and view all the answers
In Izzie's garden problem, if the two equal sides have a length $x$, what is the length of the third side?
In Izzie's garden problem, if the two equal sides have a length $x$, what is the length of the third side?
Signup and view all the answers
Study Notes
Elementary Algebra - Linear Equations in One Variable (LEOV)
- Topic: Solving problems involving linear equations in one variable.
- Concept: Finding angles within triangles, specifically focusing on the sum of angles in a triangle (m∠1+ m∠2+ m∠3 = 180°).
-
Example 1: In a right triangle, one angle (other than the right angle) is double the other.
- Step 1: Identify the known facts (right triangle, one angle is twice the other).
- Step 2: Define variables (e.g., x = smaller angle, 2x = larger angle).
- Step 3: Form an equation using the known fact that angles in a triangle sum to 180° : 90 + x + 2x = 180.
- Step 4: Solve the equation for x (x = 30).
- Step 5: Determine the other angle(s) (2x = 60), and confirm that the answer satisfies the original conditions. The angles should be 30°, 60°, and 90°.
-
Example 2: Complementary Angles (two angles whose sum is 90°). An angle is 16° more than its complement.
- Step 1: Identify complementary angles and difference between the two given angles.
- Step 2: Define variables (x = complementary angle, x + 16 = another angle).
- Step 3: Form an equation using the concept of complementary angles (x + x + 16 = 90°).
- Step 4: Solve for the unknown variable (x = 37°).
- Step 5: Determine the other angle (37° + 16° = 53°.) And verify the solution by checking if the sum is equal to 90°.
-
Example 3: Supplementary Angles (two angles whose sum is 180°). One angle is 12° more than 6 times the other.
- Step 1: Identify supplementary angles and difference between the two given angles.
- Step 2: Define variables (x = one angle, 6x + 12 = other angle).
- Step 3: Form an equation (x + 6x + 12 = 180°).
- Step 4: Solve for x (2x = 168, so x = 24).
- Step 5: Determine the other angle (6x + 12 = 156), and confirm the solution satisfies the condition of the problem.
Additional Problem Solving Tips
- Read and understand: Carefully analyze the given problem to identify the known facts and unknowns.
- Represent the unknowns: Define variables to represent the unknown quantities in the problem.
- Equation formation: Create an equation based on the given facts and relationships between the known and unknown quantities.
- Solve for the unknowns: Use mathematical operations to determine the values of the variables/unknowns.
- Interpret and check: Interpret the solution in context and verify if it aligns with all conditions of the problem.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your understanding of solving linear equations in one variable through various geometric problems. This quiz focuses on calculating angles in triangles and understanding relationships between angles. Challenge yourself with examples involving right triangles and complementary angles.
