Math Problem Statement
Steps for number 1 and 4
Solution
Let's break down and go through the steps for solving problems #1 and #4 from the image you provided.
Problem 1:
You are given a pair of intersecting lines, which form angles of 128° and . The problem asks you to identify if the angles are vertical or adjacent, and then find the value of .
Steps:
- Identify the relationship: Since the angles are opposite each other, they are vertical angles. Vertical angles are always equal.
- Set up the equation: The two angles must be equal:
- Solution: Since the angles are equal, .
The work shown in the image matches this reasoning.
Problem 4:
In this problem, there are two adjacent angles given as and . The sum of these two angles forms a straight line, meaning they are supplementary angles.
Steps:
- Recognize the relationship: Adjacent angles that form a straight line are supplementary, meaning their sum is 180°.
- Set up the equation: The sum of the two angles must equal 180°:
- Solve for : Divide both sides by 6:
So, .
Both problems involve identifying the relationship between angles (vertical or adjacent) and using basic angle properties like equality and supplementary angles to solve for .
Do you have any questions, or would you like further details on any of these steps?
Here are 5 questions related to this concept to expand your understanding:
- What is the difference between vertical and adjacent angles?
- How would you solve for if the angles formed a right angle instead of a straight line in problem 4?
- What property do complementary angles have, and how does it differ from supplementary angles?
- How do you solve for an unknown angle in a triangle if two angles are given?
- If two angles are labeled as and , and they form a straight line, what is the value of ?
Tip: Always double-check if angles are supposed to be equal or if they sum to a particular value, like 90° (right angles) or 180° (straight lines).
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Math Problem Analysis
Mathematical Concepts
Geometry
Angles
Supplementary Angles
Vertical Angles
Formulas
Vertical angles are equal: angle1 = angle2
Supplementary angles: angle1 + angle2 = 180°
Theorems
Vertical Angle Theorem
Supplementary Angle Theorem
Suitable Grade Level
Grades 7-9