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Course: Geometry A
Unit: Foundations of Euclidean Geometry
Assignment: Project: Special Angle Pairs
In Geometry, you will learn about a lot of Special Angle Pairs. In this project, you are going to look at a map, and list some of the Special Angle Pairs you find. You will also look at some other special angle pairs and find missing values as well. Please use the map below to answer questions 1-5. (Please note, this map is not drawn to scale.)
Here is a video to help before you begin: https://youtu.be/YsFsb0gb55w
Picture without trains:
- Using the diagram above, please list 4 pairs of linear angles.
∠1 and ∠ 3 ∠2 and ∠ 4 ∠5 and ∠ 7 ∠6 and ∠ 8
Angle 7 = Not able to be found Angle 8 = Not able to be found
1 point for each correct answer Total Points Earned 0 /
Note:
The questions following are individual and do not pertain to the degrees
found in question
- Using the map above, if angle 1 is 5x - 6 and angle 4 is 4x + 14, find the value of x and find the value of angle 1. Please show all your work for full credit (Hint: are the angles linear pair or vertical? Apply the concept)
5x - 6 = 4x + 14
x - 6 = 14 Add 6 to both sides: x = 20
Angle 1 = 5x - 6 = 5(20) - 6 = 100 - 6 = 94 degrees
The value of x is 20 and the measure of angle 1 is 94 degrees
Correct answer for x and < 1, and work shown (4 points)
Correct answer for both, but no work shown. Or Work is shown but only correct answer for x or < 1. (2 points)
Answer incorrect/not answered (0 points)
Total Points Earned
- Using the map above, if angle 2 is 2x + 4 and angle 6 is x + 14, find the value of x and find the measure of angle 6. Please show all your work for full credit.
(2x + 4) + (x + 14) = 180
3x + 18 = 180
Subtract 18 from both sides: 3x = 162
Divide both sides by 3: x = 54
Angle 6 = x + 14 = 54 + 14 = 68 degrees
The value of x is 54 and the measure of angle 6 is 68 degrees
Correct answer for x and < 6, and work shown (4 points)
Correct answer for both, but no work shown. Or Work is shown but only correct answer for x or < 6. (2 points)
Answer incorrect/ not answered (0 points)
Total Points Earned
- For this question, please use the image below to answer the question. If the measure of angle AEB is 112 degrees, find the measure of angle BEC. Please show all your work below for full credit. (Note: the image is not drawn to scale)
- For this question, please use the image below to answer the question. If the measure of angle 5 is 68 degrees, find the measure of angle 1. Please show all your work below for full credit. (Note: the image is not drawn to scale)
First you gotta identify the relationship between the angles: Angles 1 and 5 are vertical angles
This means they share a common vertex and their sides form two pairs of opposite rays
Understand the property of vertical angles: Vertical angles are always congruent, meaning they have the same measure
Use the given information: We know that angle 5 is 68 degrees
Lastly apply the property of vertical angles: Since angle 1 is vertical to angle 5, they have the same measure
So, the measure of angle 1 is also 68 degrees
Correct answer and work shown (4 points)
Correct answer, but no work shown (2 points)
Answer incorrect/ not answered (0 points) Total Points Earned 0 /
- For this question, please use the image below to answer the question. If the measure of angle RSU is 4x - 12 degrees, and the measure of UST is 2x - 6, find the value of x and the measure of angle RSU. Please show all your work below for full credit. (Note: the image is not drawn to scale)
First we gotta identify the relationship between the angles: Angles RSU and UST form a right angle, which measures 90 degrees
Set up an equation: We can write an equation based on the information: Angle RSU + Angle UST = 90°
Substitute the given expressions: (4x - 12) + (2x - 6) = 90°
Combine like terms: 6x - 18 = 90° Solve for x: Add 18 to both sides: 6x = 108°
Divide both sides by 6: x = 18°
Lastly substitute x = 18 into the expression for angle RSU: Angle RSU = 4x - 12 = 4(18) - 12 = 72 - 12 = 60°
So, the value of x is 18, and the measure of angle RSU is 60 degrees
Correct answer and work shown (4 points)
Correct answer, but no work shown (2 points)
Answer incorrect/ not answered (0 points) Total Points Earned 4/
- We know that in math some special angle pairs like vertical angles are congruent or equal. Using at least 3 sentences, what type of things in the Bible are considered equal in God’s eyes? Please support your answer with at least 1 Bible verse.
I think we can compare angles in math to people in the Bible. Just like vertical angles are equal, God sees all people as equal. No matter our skin color, wealth, or social status, we are all equally loved and valued by God. As it says in Galatians 3:28, "There is neither Jew nor Gentile, neither slave nor free, nor is there male and female, for you are all one in Christ Jesus."
