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"A and B are vertical angles. If m A = (x + 23)° and mB = (5x + 9), then find the measure of B.

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Final answer:

Vertical angles are equal, so by setting the angular expressions for angles A and B equal and solving for x, we find x=3.5. Substituting x=3.5 into the equation for angle B, we find that the measure of angle B is 26.5°.

Step-by-step explanation:

In mathematics, vertical angles are pairs of opposite angles formed when two lines intersect. Importantly, vertical angles are always equal. Therefore, in your question, we can set the measures of angles A and B equal to each other.

This gives us the equation: (x + 23)° = (5x + 9)°

To solve for x, we'll first subtract x from both sides of the equation, which yields: 23 = 4x + 9

Subtracting 9 from both sides gives: 14 = 4x. Divide both sides by 4 to find: x = 14 / 4 = 3.5

Substitute x = 3.5 into the equation for m B, we get: B = 5(3.5) + 9 = 17.5 + 9 = 26.5°.

So, the measure of angle B is 26.5°.

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