Math Hexagon Measure Questions

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Question 1 A) Four of the interior angles of a hexagon measure 92° , 100°, 94° , and 140°. The remaining two angles each measure (x − 32) ° . What is the value of x? Justify your response. (1 point) The sum of all interior angle measure is 720°, so each angle measuring (x − 32) ° has a measure of 294°. Thus, (x − 32) ° = 294° , and so x = 326. The sum of all interior angle measure is 540°, so each angle measuring (x − 32) ° has a measure of 246°. Thus, (x − 32) ° = 246° , and so x = 275. The sum of all interior angle measure is 720°, so each angle measuring (x − 32) ° has a measure of 147°. Thus, (x − 32) ° = 147° , and so x = 179. The sum of all interior angle measure is 540°, so each angle measuring (x − 32) ° has a measure of 123°. Thus, (x − 32) ° : Question 2 = 123° , and so x = 155. A) In the given figure, what is the measure of ∠DCI ? (1 point) ∡DCI = 71.8 ∡DCI = 70° ∡DCI = 251.8 ∡DCI = 108.2° : Question 3 Question 3 A) Quadrilateral ABCD is given with ∡A = 35° , ∡B = 40°, ∡C = (5x + 5) ° , and ∡D = (5x) ° . What is the value of x? (1 point) x = 28 x=7 x = 10 x=6 Question 4 : A) Are the two triangles depicted similar? Explain. (1 point) The two triangles are not similar since a dilation does not preserve the interior angle measures of a triangle. The two triangles are similar since a dilation of △ABC , with the origin as the center of dilation and a scale factor of 1 , maps it onto △DEF . 3 The two triangles are similar since a dilation of △ABC , with the origin as the center of dilation and a scale factor of 3 , maps it onto △DEF . : The two triangles are not similar since a dilation does not preserve the side lengths of a triangle. Question 5 A) △ABC has m∠B = 25° , AB = 3 , and BC = 4 . Which of the following triangles is similar to △ABC ? Explain. (1 point) △DEF with m∠E = 25°, DE = 16, and EF = 12 is similar to △ABC by the side-angle-side (SAS) similarity criterion. △DEF with m∠E = 25°, m∠D = 45° , and m∠F = 110° is similar to △ABC by the angle-angle (AA) similarity criterion. △DEF with m∠E = 25°, m∠D = 65° , and m∠F = 90° is similar to △ABC by the angle-angle (AA) similarity criterion. △DEF with m∠E = 25°, DE = 12, and EF = 16 is similar to △ABC by the side-angle-side (SAS) similarity criterion. : Question 6 Question 6 A) Two triangles, △QRS and △U T S , are given with a common vertex, S . If ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯ QR ∥ T U such that ∠QRS , is congruent to ∠ST U which of the following is true? (1 point) RS ⋅ QR = SU ⋅ ST RS ⋅ T U = QR ⋅ ST QR ⋅ QS = ST ⋅ SU QR ⋅ SU = QS ⋅ ST Question 7 : A) Which of the following would prove that △AED is similar to △ABC in the given figure? Select the two correct answers. (1 point) Reflect △AED across x = 0 and then across y = 0 . Dilate △AED with the origin as the center of dilation using a scale factor of 3 . Reflect △AED across y = 0 and then across x = 0 . Dilate △AED with the origin 1 as the center of dilation using a scale factor of 3 . 180° about the origin. Dilate △AED with the origin as the center of dilation using a scale factor of 3 . : Rotate △AED Rotate △AED 270° clockwise about the origin. Dilate △AED with the origin as the center of dilation using a scale factor of 1 . 3 Rotate △AED 180° about the origin. Dilate △AED with the origin as the center of dilation using a scale factor of 1 . 3 Question 8 A) : A carpenter constructs a table with four legs that each forms an acute angle with the tabletop. Each leg is 3 feet long, and the distance from the edge of the tabletop to the point at which each leg connects is 6 inches. What is the height of the table? Round your answer to the nearest hundredth of a foot. (1 point) 2.96 feet 2.85 feet 5.20 feet 3.04 feet Question 9 A) A loading ramp is extended from the back of a truck to form a 30° angle with the ground. The truck and the ramp are both on level ground. If the length of the ramp is x feet, how high is the back of the truck from the ground? (1 point) x√3 feet 2 x feet 2 2x feet x√3 feet : Question 10 Question 10 A) △ABC is given with a right angle, ∠B , cos(3x + 30)° = sin(12x)° . If ∡A = (3x + 30) ° , what is the value of ∡A? Explain. (1 point) ∡A = 42° since 3x + 30 + 12x = 90 and x = 4. ∡A = 48° since 3x + 30 + 12x = 90 and x = 4. ∡A = 60° since 3x + 30 = 12x and x = 10 . ∡A = 40° since 3x + 30 = 12x and x = Question 11 : A) 10 . 3 ←→ In the figure provided, ⊙A is given with a radius of 3 , BC = 4 , and CB tangent to ⊙A at B . Can it be concluded that AC = 5 ? Explain. (1 point) = 5. Since AB = 3 and BC = 4, the triangle must be right, and so the remaining side length must be 5 . Yes, AC No, AC does not necessarily equal 5 . It cannot be determined that ∠ABC is right. No, AC does not necessarily equal 5 . Although the triangle is a right triangle, AC can be a range of values. = 5. Since ∠ABC is right, the triangle is right, and so the remaining side length must be 5 . : Yes, AC Question 12 A) In ⊙P , AB is drawn through P , and ¯¯¯¯¯¯¯¯ AC and ¯¯¯¯¯¯¯¯ P C are drawn as well with A, B , and C falling on the circumference of ⊙P . If the measure of ⌢ BC is 60°, what is ∡BAC ? (1 point) ¯¯¯¯¯¯¯¯ ∡BAC = 60° ∡BAC = 15° ∡BAC = 30° ∡BAC = 120° : Question 13 Question 13 A) An equilateral triangle, △ABC , has been inscribed in ⊙O . Which of the following constructions would result in the regular hexagon inscribed in ⊙O ? (1 point) Three points are taken on the circumference of ⊙O such that any one point is equally distant from the other two. These points are joined in succession with the vertices of △ABC to form the regular hexagon inscribed within ⊙O . Three diameters are drawn through the center of ⊙O such that each diameter forms a 30° angle with the other two. The points of the diameters on the circumference of ⊙O are joined in succession with the vertices of △ABC to form the regular hexagon inscribed within ⊙O . Three radii are drawn from the center of ⊙O such that each radius forms a 60° angle with each of the other two radii. The points of the radii on the circumference of ⊙O are joined in succession with the vertices of △ABC to form the regular hexagon inscribed within ⊙O . The arc intercepted by each pair of vertices in △ABC is bisected, and these points are joined in succession with the vertices of the triangle to form the regular hexagon inscribed within ⊙O . : Question 14 Question 14 A) Quadrilateral QRST is inscribed within ⊙A with ∡Q = (2x + 5) °, ∡R = (x + 17) ° , ∡S = ( x−5 2 ) ° , and ∡T = (x + 21) °. Match each angle with its measure. (2 points) ∠R ∠S ∠Q ∠T ! : Question 15 33° ! 147° ! 88° ! 92° Question 15 A) A circle is given with the equation x2 + y 2 − 8x + 6y + 19 = 0 . What is the equation of the circle in standard form? Explain. (1 point) x2 + y 2 − 8x + 6y + 19 = 0 can be rewritten as x2 − 8x + y 2 + 6y = 0. 2 2 Completing the square yields (x − 4) + (y + 3) = 25. x2 + y 2 − 8x + 6y + 19 = 0 can be rewritten as x2 − 8x + y 2 + 6y = 0. 2 2 Completing the square yields (x − 4) + (y + 3) = 100 . x2 + y 2 − 8x + 6y + 19 = 0 can be rewritten as x2 − 8x + y 2 + 6y = −19. 2 2 Completing the square yields (x − 4) + (y + 3) = 81. x2 + y 2 − 8x + 6y + 19 = 0 can be rewritten as x2 − 8x + y 2 + 6y = −19. 2 2 Completing the square yields (x − 4) + (y + 3) = 6 . Question 16 : A) In the given figure, ⊙B is drawn with ∡ABC = 53° . If BC = 9 , what is the area of ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ the sector formed by BA , BC , and the intercepted arc? Round your answer to the nearest tenth. (1 point) 8.3 square units 74.9 square units 16.7 square units 37.5 square units : Question 17 Question 17 A) Leah takes a square-base pyramid and takes a cross section perpendicular to its base. She notes that this cross section is triangle and any cross section taken of a square-base pyramid will be a triangle. Is Leah correct? Explain. (1 point) Leah is correct. Taking a cross section parallel to the base of the square-base pyramid will result in a triangle as well. Leah is not correct. Taking a cross section parallel to the base of the square-base pyramid will result in a square. Leah is correct. Taking any cross section that is not perpendicular to the base will also result in a triangle. Leah is not correct. Taking a cross section of a square-base pyramid perpendicular to its base produces a square, not a triangle. : Question 18 A) △ABC is rotated around the line x = 0 to produce a solid. Which of the following describes the shape of the solid? (1 point) The solid is a cone. The solid is a cone with a cylinder removed from within The solid is a cylinder with a cone removed from within. The solid is a cylinder. : Question 19 Question 19 A) A silo is to be constructed so that a farmer can store grain inside it. The silo is designed to have the shape of a cylinder. If the height of the silo is 20 feet and the farthest distance between the silo's walls is 6 feet, what is the volume of the silo? Round your answer to the nearest tenth of a cubic foot. (1 point) 565.5 cubic feet 377.0 cubic feet 188.5 cubic feet 2, 261.9 cubic feet : Question 20 Question 20 A) Theresa and Angel are debating whether snow cones or ice cream cones are a greater value. One snow cone can be purchased for the same price as one ice cream cone, but Angel argues that the snow cone is better since it has a greater density than the ice cream cone. Both cones have a radius of 1.5 inches and a height of 3 inches, and the snow cone and ice cream cone weigh 4 ounces and 6 ounces, respectively. Assuming that the cones are filled precisely with no overflow, is Angel correct? Explain, rounding values to the nearest tenth of an ounce per cubic inch. (1 point) Angel is not correct since the density of the snow cone is 0.8 ounces per cubic inch, while the density of the ice cream cone is 1.3 ounces per cubic inch. Angel is correct since the density of the snow cone is 1.8 ounces per cubic inch, while the density of the ice cream cone is 1.2 ounces per cubic inch. Angel is correct since the density of the snow cone is 1.2 ounces per cubic inch, while the density of the ice cream cone is 0.8 ounces per cubic inch. Angel is not correct since the density of the snow cone is 0.6 ounces per cubic inch, : while the density of the ice cream cone is 0.8 ounces per cubic inch.
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