# Section 8.1 Objective: Students will be able to solve equations to find angle measures (supplementary and complementary).

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1 Lincoln Public Schools Math 8 McDougall Littell Middle School Math Course 3 Chapter 8 Items marked A, B, C are increasing in difficulty. Group A questions are the most basic while Group C are the most difficult and require higher levels of thinking skills. The level of difficulty is only relative to the same section. Most problems include random number generation within individual problems. [n] indicates n problems types are available in the topic. Note: Some problems use text boxes for fractions. For these problems, do not enter spaces before or after the numeric values. Do not enter the % symbol into a numeric box when solving for percents. Section 8.1 Objective: Students will be able to solve equations to find angle measures (supplementary and complementary). 8_1 MC Supplementary/Complementary [3] Multiple choice to determine if two angles are supplementary, complementary or neither. 8_1 Find Supplement/Complement [2] one angle, find the supplement or complement. 8_1 Find Angle Measures A [2] Use complementary, supplementary and vertical angles to solve for multiple angles. (Inline Question). 8_1 Find Angle Measures B [2] Use complementary, supplementary and vertical angles to solve for multiple angles from complex drawings. (Inline Question). 8_1 Find Angle Measures C [2] Use alternate interior, alternate exterior, vertical angles, and corresponding angles to solve for multiple angles. (Inline Question). Section 8.2 Objective: Students will be able to solve equations to find angle measures. 8_2 Classify Triangles [2] Classify triangles as scalene, isosceles, equilateral, acute, obtuse, and right. (Matching). 8_2 Solve for an Angle A [3] Solve for a missing angle in three types of triangles. 8_2 Solve for an Angle B [3] Solve for the angle with variables in more than one angle. 8_2 Solve for an Angle C [2] Solve for the largest angle after solving for one angle of a triangle. Section 8.3 Objective: Students will be able to classify quadrilaterals and find the sum of angle measures in quadrilaterals. 8_3 Classify Quadrilaterals [1] Matching quadrilaterals to their classification of parallelogram, rhombus, square, rectangle, and trapezoid. 8_3 Solve Quadrilateral Angle A [2] Solve for a missing angle of a quadrilateral. 8_3 Solve Quadrilateral Angle B [3] Solve for multiple missing angles.

2 Lincoln Public Schools Math 8 McDougal Littell Middle School Math Course 3 Please note: This demo is a one problem sample from each topic. Most problems are random number problems and consist of multiple types for each topic. Some fraction problems are not properly formatted in this demo due to the conversion to Word form. They will appear properly formatted when used in EDU. 8_1 MC Supplementary/Complementary [3] Multiple choice to determine if two angles are supplementary, complementary or neither. Determine if 1 and 2 are supplementary, complementary, or neither given: 1 = 57 and 2 = 123 Your Answer: Supplementary Correct Answer: Supplementary Determine if 1 and 2 are supplementary, complementary, or neither given: 1 = 57 and 2 = = = 180 Since the angles add to 180, they are supplementary angles. 8_1 Find Supplement/Complement [2] one angle, find the supplement or complement. 1 and 2 are supplementary. Determine the 2 if 1 = 59. Do not enter a degree symbol in the answer box. Your Answer: 121 Correct Answer: and 2 are supplementary. Determine the 2 if 1 = 59. Supplementary angles add to =180 2 = 121

3 8_1 Find Angle Measures A [2] Use complementary, supplementary and vertical angles to solve for multiple angles. (Inline Question). Your response Correct response 1 = 139, find: 1 = 139, find: 2 = 41 (33%) 3 = 139 (33%) 4 = 41 (33%) Do not enter the degree symbol into the answer box. 2 = 41 3 = = 41 Do not enter the degree symbol into the answer box. 1 = a1, find: 1 and 2 are supplementary = = = 41 1 and 3 are vertical angles. 3 = 1 = and 4 are vertical angles. 4 = 2 = 41

4 8_1 Find Angle Measures B [2] Use complementary, supplementary and vertical angles to solve for multiple angles from complex drawings. (Inline Question). Your response Correct response 4 = 59, find: 4 = 59, find: 3 = 31 (50%) 5 = 90 (50%) Do not enter the degree symbol into the answer box. 3 = 31 5 = 90 Do not enter the degree symbol into the answer box. 4 = 59, Since 2 is a right angle, the lines forming this angle are perpendicular and all angles between these two lines are 90. The 5 = and 4 are complementary angles adding to = = 90 3 = 31

5 8_1 Find Angle Measures C [2] Use alternate interior, alternate exterior, vertical angles, and corresponding angles to solve for multiple angles. (Inline Question). Your response Correct response 1 = 42, find: 1 = 42, find: 3 = 42 (25%) 4 = 138 (25%) 5 = 42 (25%) 6 = 138 (25%) Do not enter the degree symbol into the answer box. 3 = 42 4 = = 42 6 = 138 Do not enter the degree symbol into the answer box. 1 = 42, 1 and 3 are corresponding angles with equal measures. 3 = 1 = 42 3 and 4 are supplementary angles adding to = = = and 5 are vertical angles with equal measures.

6 5 = 3 = 42 4 and 6 are vertical angles with equal measures. 6= 4 = 138 8_2 Classify Triangles [2] Classify triangles as scalene, isosceles, equilateral, acute, obtuse, and right. (Matching). All the items matched correctly. Match Your Choice Correct Choice obtuse obtuse acute acute right right Classify the triangles. Match each triangle to its classification. right contains one right angle obtuse contains one angle greater than 90

7 acute all angles are less than 90 8_2 Solve for an Angle A [3] Solve for a missing angle in three types of triangles. y 16 Solve for y in the triangle above. Do not enter the symbol in the answer box. Your Answer: 74 Correct Answer: 74 y 16 Solve for y in the triangle above. Do not enter the symbol in the answer box. The interior angles of a triangle sum to 180. y = 180 y + 16 = 90 (The acute angles of a right triangle sum to 90.) y = 74

8 8_2 Solve for an Angle B [3] Solve for the angle with variables in more than one angle. y (5y + 6) 18 Solve for y in the triangle above. Do not enter the symbol in the answer box. Your Answer: 26 Correct Answer: 26 y (5y + 6) 18 Solve for y in the triangle above. Do not enter the symbol in the answer box. The interior angles of a triangle sum to 180. y + (5y + 6) + 18 = 180 (6y + 24) = 180 6y = 156 y = 26 8_2 Solve for an Angle C [2] Solve for the largest angle after solving for one angle of a triangle. y (5y + 21) 27 Solve for the largest angle in the triangle above. Do not enter the symbol in the answer box. Your Answer: 131 Correct Answer: 131

9 y (5y + 21) 27 Solve for the largest angle in the triangle above. Do not enter the symbol in the answer box. The interior angles of a triangle sum to 180. y + (5y + 21) + 27 = 180 (6y + 48) = 180 6y = 132 y = 22 The other angle is (5y + 21) = ( ) = 131 The largest angle of the three angles is 131 8_3 Classify Quadrilaterals [1] Matching quadrilaterals to their classification of parallelogram, rhombus, square, rectangle, and trapezoid. All the items matched correctly. Match Your Choice Correct Choice Square Square Rhombus Rhombus Rectangle Rectangle

10 Trapezoid Trapezoid Parallelogram Parallelogram Classify each quadrilateral. Match each quadrilateral with the appropriate type. Parallelogram Both pairs of opposite sides are parallel. Rectangle Four right angles Rhombus Four sides of equal length. Square Four sides of equal length and four right angles. Trapezoid Exactly one pair of parallel lines.

11 8_3 Solve Quadrilateral Angle A [2] Solve for a missing angle of a quadrilateral a Find the angle a. Do not enter the symbol into the answer box. Your Answer: 107 Correct Answer: a Find the angle a. Do not enter the symbol into the answer box. The sum of the interior angles of a quadrilateral is a = a = 360 a = 107

12 8_3 Solve Quadrilateral Angle B [3] Solve for multiple missing angles. Your response Correct response a a b b Find the measures of angles a and b Do not enter the symbol into the answer box. a = 49 (50%) b = 131 (50%) Find the measures of angles a and b Do not enter the symbol into the answer box. a = 49 b = 131 a b Find the measures of angles a and b Do not enter the symbol into the answer box. The sum of the interior angles of a quadrilateral is a = a = 360 a = 49 a and b are supplementary angles. a + b = b = 180 b = 131

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