Question

[20 pts] Hi! Could I please get some help? Using the map above, assuming that Browning St and Old St are parallel, if angle 1 is 2x + 8, and angle 8 is x + 10, find the value of x and find the measure of angle 8. Please show all your work for full credit. (On the map, angles 1 and 8 are diagonal from each other)

Answer 1

The value of x is 54 and the measure of angle 8 is 64 degrees

How to determine the value of x and find the measure of angle 8?

The given parameters are

Angle 1 = 2x + 10

Angle 8 = x + 10

The figure that completes the question is added as an attachment

From the figure, we have

Angle 1 = Angle 3 ---- vertical angles

Angle 3 + Angle 8 = 180 ---- internal angles within the transversal

Substitute Angle 1 = Angle 3 in the equation Angle 3 + Angle 8 = 180

Angle 1 + Angle 8 = 180

Substitute the known values in the above equation

2x + 8 + x + 10 = 180

Evaluate the like terms

3x = 162

Divide both sides by 3

x = 54

Substitute x = 54 in Angle 8 = x + 10

Angle 8 = 54 + 10

Evaluate

Angle 8 = 64

Hence, the value of x is 54 and the measure of angle 8 is 64 degrees

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