Hard - Quiz 1

Combine parallel line theorems, similar triangle algebra, exterior angle equations, midsegment properties, and multi-step angle chasing in complex figures.

Question 1 of 5

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Question 1

Lines \(\ell\) and \(m\) are parallel. A transversal crosses line \(\ell\) at point \(A\) and line \(m\) at point \(C\). A point \(B\) lies between the two parallel lines, forming triangle \(ABC\). If the angle at \(A\) between the transversal and side \(AB\) is 70° and angle \(B\) is 40°, what is the measure of angle \(C\)?

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Triangles \(PQR\) and \(STU\) are similar. In triangle \(PQR\), \(PQ = 3\) and \(QR = 4\). In triangle \(STU\), \(TU = 8\). If \(QR\) corresponds to \(TU\), what is the length of \(ST\)?

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In a triangle, one exterior angle measures \((5x - 10)\)° and the two non-adjacent interior angles measure \((2x + 5)\)° and \((x + 15)\)°. What is the measure of the exterior angle?

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In triangle \(ABC\), the segment connecting the midpoints of sides \(AB\) and \(AC\) is called a midsegment. If \(BC = 22\) cm, what is the length of this midsegment?

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In triangle \(ABC\), angle \(A = 35°\). Point \(D\) lies on side \(AC\) such that \(BD\) is perpendicular to \(AC\). If angle \(DBC = 20°\), what is the measure of angle \(C\)?

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