16. Which is the sum of the exterior angle measures of a 100-sided polygon A. 180° B. 360° C. 3,600° D. 7,200° 17. How many sides does a polygon have if its interior angle measures add up to 4,140°? A. 14 B. 25 C. 36 D. 47 18. Which is the measure of each interior angle of a regular 16-sided polygon? A. 22.5° B. 85° C. 157.5° D. 180° 19. Which of the following statements is NOT true when the number of sides of a polygon increases? A. The number of diagonals increases. B. The number of vertices increases. C. The sum of the interior angle measures increases. D. The sum of the exterior angle measures increases. 20. Which of the following statements is true if two angles are complementary? A. They are both acute. B. One is acute and one is right. C. One is acute and one is obtuse. D. One is right and one is obtuse. 21. Which of the following statements about vertical angles is always true? A. They are complementary. B. They are supplementary. C. They are right angles. D. They are congruent. 22. Which of the following statements is NEVER true? A. Adjacent angles are complementary. B. Vertical angles form a linear pair. C. Congruent angles are supplementary. D. Adjacent angles are congruent.
Answer (1)
Answer:Let's go through each question: 16. B. 360° The sum of the exterior angles of any polygon is always 360°.17. B. 25 The formula for the sum of interior angles of an n-sided polygon is (n-2) * 180°. Solving (n-2) * 180° = 4140° for n gives n = 25.18. C. 157.5° The sum of the interior angles of a 16-sided polygon is (16-2) * 180° = 2520°. Each interior angle of a regular 16-sided polygon is 2520° / 16 = 157.5°.19. D. The sum of the exterior angle measures increases. The sum of the exterior angles of any polygon is always 360°.20. A. They are both acute. Complementary angles add up to 90°. If the sum is 90°, neither angle can be 90° or greater.21. D. They are congruent. Vertical angles are the angles opposite each other when two lines intersect. They are always congruent (equal in measure).22. D. Adjacent angles are congruent. Adjacent angles share a common vertex and side. They don't have to be congruent (equal); they could be any combination of angles that add up to any value.
