Medium - Quiz 1

Apply parallel line angle relationships, the triangle inequality, similar triangle proportions, and algebraic angle problems to more involved setups.

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Question 1

Lines \(p\) and \(q\) are parallel, and a transversal crosses both lines. The transversal makes a 55° angle with line \(p\). What is the measure of the alternate interior angle at line \(q\)?

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Two sides of a triangle have lengths 7 and 11. Which of the following could be the length of the third side?

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Triangle \(ABC\) is similar to triangle \(DEF\). In triangle \(ABC\), \(AB = 6\) and \(BC = 9\). In triangle \(DEF\), \(DE = 10\). What is the length of \(EF\)?

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Two parallel lines are cut by a transversal. One of the co-interior (same-side interior) angles measures \((3x + 10)\)° and the other measures \((2x + 20)\)°. What is the value of \(x\)?

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Two triangles share a common side. Each triangle also has a pair of angles equal to the corresponding pair in the other triangle. Which congruence criterion applies?

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