Communicate Mathematical Ideas In the diagram at the right, suppose m\(\angle\)6 = 125°. Explain how to find the measures of each of the other seven numbered angles.
Draw Conclusions In a diagram showing two parallel lines cut by a transversal, the measures of two same-side interior angles are both given as 3x°. Without writing and solving an equation, can you determine the measures of both angles? Explain. Then write and solve an equation to find the measures.
Make a Conjecture Draw two parallel lines and a transversal. Choose one of the eight angles that are formed. How many of the other seven angles are congruent to the angle you selected? How many of the other seven angles are supplementary to your angle? Will your answer change if you select a different angle?
Critique Reasoning In the diagram at the right, \(\angle 2\),\(\angle 3\),\(\angle 5\), and\(\angle 8\) are all congruent, and\(\angle 1\),\(\angle 4\), \(\angle 6\), and \(\angle 7\) are all congruent. Aiden says that this is enough information to conclude that the diagram shows two parallel lines cut by a transversal. Is he correct? Justify your answer.
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