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Given that m∠A = (17x)º, m∠C = (8x + 23)º, and m∠D = 122º, what is m∠B?

User Ory Band
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1 Answer

3 votes

Answer:

To find m∠B, we will need to use the fact that the sum of the angles in a quadrilateral is 360 degrees.

m∠A + m∠B + m∠C + m∠D = 360º

Substituting the given values, we get:

(17x)º + m∠B + (8x + 23)º + 122º = 360º

Simplifying and solving for m∠B:

25x + 145º = 360º

25x = 215º

x = 8.6

Substituting x back into the equation:

m∠A = (17x)º = (17)(8.6)º = 146.2º

m∠C = (8x + 23)º = (8)(8.6)º + 23º = 95.8º

Now we can find m∠B:

(17x)º + m∠B + (8x + 23)º + 122º = 360º

146.2º + m∠B + 95.8º + 122º = 360º

m∠B = 360º - 364º

m∠B = -4º

However, an angle cannot be negative, so this means that there is no solution that satisfies the given conditions. It is possible that there is a typo or mistake in the problem statement.

User Mangecoeur
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