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Geometry Chapter 6 Study Guide 1. Find sum of the interior angle of a 26-gon. 2. Find the number of sides of a regular polygon with an interior angle measure of 162 ̊ 3. Find the measure of each exterior angle of a regular dodecagon. 4. Find the measure of each interior angle of a regular polygon with 20 sides. 5. Using PATS fill in the blanks. P a. If SA = 88, then SL = ___________ A L b. If STP = 33o, then APT = ___________ S c. If ST = 110 then AP = _______________ T 6. ABCD is a parallelogram. Find the value of each variable. x= 57 A B y= 125 o 73 8a + 17 xo D 5b + 12 yo C a= b= 7. The length of one base of a trapezoid is 30 and the median is 22. Find the length of the other base. 8. JKLM is an isosceles trapezoid. 24 J K 48 ̊ M Find the median, ∠M, and ∠J. L 38 9. For the rhombus, find x and y y 6x 35 ̊ 10. The diagonals of square QRST intersect at point P. If 𝑄𝑃 = 2𝑥 + 8 and 𝑅𝑃 = 5𝑥 − 4, find QS. 11. In the parallelogram, find m∠1, m∠2 and m∠3 1 2 85 ̊ 53 ̊ 3 12. In the rectangle, find m∠1. 1 (4x+23)̊ (6x-5)̊ 13. ABCD is a rectangle. 𝐴𝐶 = 𝑥 2 − 𝑥 and 𝐵𝐷 = 4𝑥 + 14 Find x and the length of each diagonal. 14. State TRUE or FALSE for each statement: A. Diagonals are congruent in a rectangle but not in a parallelogram. __________ B. All four sides are congruent in a rhombus but not a parallelogram. __________ C. Diagonals are perpendicular in a rhombus but not in a square. __________ D. Diagonals bisect both angles in a square but not in a rectangle. _________ 15. A convex pentagon has interior angles with measures (2x 15)°, (6x 110)°, (5x 20)°, (4x 35)°, and (3x 50)°. Find the measure of each interior angle. 16. Given the set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square. Explain your reasoning. A(1, 5) B(6, 5) C(6, 10) D(1, 10)