The geometric relationship, relationship between the measure of the labelled angles, and the value of x in each case are:
a. Geometric Relationship: vertical angles
Relationship of their measures: they are equal
Equation: (3x + 5) = (5x - 5)
x = 5
b. Geometric Relation: straight line angles
Relationship of their measures: their sum equals 180
Equation: (4x + 150) + 2x = 180
x = 5
a. (3x + 5) and (5x - 5) are vertical angles opposite to each other.
The geometric relationship is "vertical angles are congruent".
- This means (3x + 5) and (5x - 5) are of equal measure.
- Therefore equation from the geometric relation is:
[tex](3x + 5) = (5x - 5)[/tex]
[tex]3x + 5 = 5x - 5[/tex]
[tex]3x - 5x = -5- 5\\\\-2x = -10[/tex]
[tex]x = 5[/tex]
b. (4x + 150) and 2x are angles that lie on a straight line.
Angles on a straight line are supplementary and will add up to give you 180 degrees.
The geometric relationship is therefore "angles on a straight line are supplementary".
- Therefore equation from the geometric relation is:
[tex](4x + 150) + 2x = 180[/tex]
[tex]4x + 150 + 2x = 180[/tex]
[tex]6x + 150 = 180[/tex]
- Subtract 150 from both sides
[tex]6x = 180 - 150\\\\6x = 30[/tex]
Divide both sides by 6
[tex]x = 5[/tex]
Therefore, the geometric relationship between the given measures of the angles, their equation from the relation and the x value of each are:
a. Geometric Relationship: vertical angles
Relationship of their measures: they are equal
Equation: (3x + 5) = (5x - 5)
x = 5
b. Geometric Relation: straight line angles
Relationship of their measures: their sum equals 180
Equation: (4x + 150) + 2x = 180
x = 5
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