Math Problem Statement

Steps for number 1 and 4

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 xx. The problem asks you to identify if the angles are vertical or adjacent, and then find the value of xx.

Steps:

  1. Identify the relationship: Since the angles are opposite each other, they are vertical angles. Vertical angles are always equal.
  2. Set up the equation: The two angles must be equal: x=128x = 128^\circ
  3. Solution: Since the angles are equal, x=128x = 128^\circ.

The work shown in the image matches this reasoning.


Problem 4:

In this problem, there are two adjacent angles given as 4x4x^\circ and 2x2x^\circ. The sum of these two angles forms a straight line, meaning they are supplementary angles.

Steps:

  1. Recognize the relationship: Adjacent angles that form a straight line are supplementary, meaning their sum is 180°.
  2. Set up the equation: The sum of the two angles 4x+2x4x^\circ + 2x^\circ must equal 180°: 4x+2x=1804x + 2x = 180
  3. Solve for xx: 6x=1806x = 180 Divide both sides by 6: x=30x = 30^\circ

So, x=30x = 30^\circ.


Both problems involve identifying the relationship between angles (vertical or adjacent) and using basic angle properties like equality and supplementary angles to solve for xx.


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:

  1. What is the difference between vertical and adjacent angles?
  2. How would you solve for xx if the angles formed a right angle instead of a straight line in problem 4?
  3. What property do complementary angles have, and how does it differ from supplementary angles?
  4. How do you solve for an unknown angle in a triangle if two angles are given?
  5. If two angles are labeled as 3x3x and 5x5x, and they form a straight line, what is the value of xx?

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