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Find the measure of angle B:

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You have the following expressions for angles ∠A and ∠B:

∠A = 2x + 30

∠B = 3x - 20

In order to find the measure of angle ∠B it is necessary to solve for x.

You consider that angle ∠A and the angle just above the line are supplementary, that is, they add up 180°.

Furthermore, you consider that angle above angle ∠A is equal to angle ∠B, because the lines which cross the secant line are parallel.

Thus, what you have is that the sum of angles ∠A and ∠B is equal to 180°.

∠A + ∠B = 180 you replace by the algebraic expressions

2x + 30 + 3x - 20 = 180 simplify similar terms left side

2x + 3x + 30 - 20 = 180

5x + 10 = 180 subtract 10 both sides

5x = 180 - 10

5x = 170 divide by 5 both sides

x = 170/5

x = 34

Next, you replace the previoues value of x into the expression for angle ∠B:

∠B = 3x - 20 = 3(34) - 20 = 102 - 20 = 84

Hence, the measure of angle ∠B is 84°

User Ning Chen
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