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Angle Proof Puzzle Cards
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Angle Proof Puzzle Cards
Aaliyah and Logan are checking a trail map at a national park. Use the angle diagrams and facts on these cards to solve each puzzle. For every answer, name the angle relationship or theorem and show the equation or reasoning that proves it. Parallel lines are marked with matching arrowheads. Angles are not necessarily drawn to scale.
Puzzle Cards
Work through each card. The diagrams are included with the questions so you have all the information you need.
1.Two straight trail signs cross. ∠1 and ∠3 are opposite angles. If m∠1 = 4x + 8° and m∠3 = 6x − 22°, find x and both angle measures. State the theorem that justifies your first equation.
2.Two parallel trail routes are crossed by a straight connector. ∠2 and ∠6 occupy the same relative position at the two intersections. If m∠2 = 3x + 12° and m∠6 = 5x − 28°, find x and the measure of each angle. Name the theorem.
3.Two parallel lines are crossed by a transversal. ∠3 and ∠6 lie between the parallel lines on opposite sides of the transversal. If m∠3 = 7x − 5° and m∠6 = 4x + 40°, find x and both angle measures. Explain why the angles are equal.
4.At a trail junction, two adjacent angles form a straight line. One angle is 117° and the other is x°. Find x and give the angle relationship that proves your answer.
5.Two parallel trail boundaries are crossed by a connector. ∠4 and ∠5 are alternate interior angles. If m∠4 = 8x + 4° and m∠5 = 10x − 20°, find x and the angle measures. State the theorem used.
6.Andre says: “If two lines cross and a pair of opposite angles are both 52°, those angles are congruent because they are vertical angles.” Is his reason valid? Explain briefly.
7.Logan writes: “∠A and ∠B are adjacent and form a straight line. ∠A = 132°, so ∠B = 132° by the vertical angles theorem.” Identify the error and give the correct measure of ∠B with a valid reason.
8.Two parallel lines are crossed by a transversal. ∠P and ∠Q are corresponding angles. Fill the blank with the theorem that justifies the statement: “Since the lines are parallel, ∠P ≅ ∠Q by the theorem.”
9.Draw two parallel lines crossed by a transversal. Label one pair of alternate interior angles ∠R and ∠S. If m∠R = 5x + 15° and m∠S = 7x − 25°, write an equation, solve for x, and state m∠R and m∠S. Your drawing and explanation should show why your equation is valid.
3 printable pages
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