Geometry- examine the diagrams below. what is the geometric relationship between the labeled angles? what is the relationship of their measures? then, use the relationship to write an equation and solve for x.

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".

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".

Divide both sides by 6

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

Learn more here:

link

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation: