Multiple Choice
Given two triangles, and , if is congruent to , which of the following statements about their corresponding sides and angles is true according to the Law of Sines?
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7. Non-Right Triangles
Law of Sines
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Given that ray bisects , and and , what is the measure of ?
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Verified step by step guidance1
Understand that ray BE bisects angle ABC, which means it divides angle ABC into two equal angles: angle ABE and angle CBE.
Set up the equation expressing that angle ABE equals angle CBE, so: \$2x + 7 = 5x - 8$.
Solve the equation for \(x\) by isolating \(x\) on one side: subtract \$2x\( from both sides and add \)8\( to both sides to get \)7 + 8 = 5x - 2x$.
Simplify the equation to find \(x\): \$15 = 3x\(, then divide both sides by 3 to get \)x = 5$.
Calculate the measure of angle ABC by adding angle ABE and angle CBE using the found value of \(x\): \(\angle ABC = (2x + 7) + (5x - 8)\).
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