Address any misconceptions that may arise.Īssign the What’s the Angle? Bonus Worksheet printable for classwork or homework. Make sure students explain their mathematical thinking. Step 10: Checking for Understanding: Review the answers to the What's Your Angle? Finding Missing Angle Measurements printable, which are provided on page 1 of the Answer Key: Designing With Geometry printable. ![]() Step 9: Assign the What’s Your Angle? Finding Missing Angle Measurements printable for classwork or homework. Step 8: Checking for Understanding: Review answers as a class and respond to any questions. ∠ CBG + ∠ DBE + ∠ GBE must add up to 180º because they all "fit" on a straight line. ∠ GBE = 90º, proven with the following steps: If ∠ ABD = 45º, then ∠ DBE must also equal 45º because the two angles are complementary.∠ CBG is also 45º because it and ∠ ABD are vertical angles. ∠ ABD = 45º because it and ∠ ABC are supplementary.Ask the class to pair up and find the measurement of ∠ ABD, ∠ CBG, and ∠ GBE. Step 7: Draw the illustration above on the board or provide students with a copy. There are other paths to this solution, and, if necessary, demonstrate how the answer could be obtained using other angles in the drawing (or have student volunteers explain). What is the measurement of ∠ EBF? First, if ∠ ABD = 72º then ∠ ABE= 108º. Indicate that ∠ ABF = 58º and ∠ ABD = 72º. Step 6: Using the same drawing, add line segment BF, which creates angles ABF and FBE from angle ABE. If necessary, repeat the process to show that ∠ ABD = ∠ EBC. Using the same drawing, demonstrate that ∠ ABE = ∠ DBC and ∠ ABD = ∠ EBC. Step 5: Note that when angles are formed when lines intersect, the angles opposite each other, called vertical angles, have equal angle measurements. If ∠ ABE + ∠ EBC = 180º, then 135º + x = 180º (where x represents ∠ EBC) and we can calculate that ∠ EBC = 45º. Indicate that ∠ ABE = 135º and we want to find the measurement of ∠ EBC. Step 4: Demonstrate how we can use our knowledge of supplementary angles to find missing angle measurements. Mention that, just as with complementary angles, supplementary angles don't have to be adjacent they just have to add up to 180º. To remember the term supplementary angle, think of straight line. We know they add up to 180º because they each include sides that are part of the line AC and there are 180º in a line. For example, ∠ ABE and ∠ EBC are adjacent because they are next to each other and supplementary because their measurements add up to 180º. Two sets of adjacent supplementary angles are created. Step 3: Draw lines AC and DE that intersect at point B. Also note that complementary angles don't have to be adjacent (next to each other) they just have to add up to 90º. One way to remember the term is that complementary angles add up to 90º, and 90º angles form at corners. ![]() Note that when two angles add up to 90º, they are called complementary. How can we find the measurement of ∠ DBC? Tell the class that if ∠ ABC is a 90º angle, then ∠ ABD + ∠ DBC must also equal 90º. Step 2: Create two complementary angles by adding ∠ ABD inside the right angle. The problem indicates that the angle is part of a rectangle, right triangle, etc.The square notation is used at the vertex. ![]()
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