Geometry Textbook Questions PDF

## Textbook Questions for Section 2.4 10. LMNOP is a regular pentagon. a) Determine the measure of ∠OLN. b) What kind of triangle is ∆LON? Explain how you know. * a) 36° * b) Isosceles triangle 11. Sandy designed this logo for the jerseys worn by her softball team. She told the gr...

## Textbook Questions for Section 2.4 10. LMNOP is a regular pentagon. a) Determine the measure of ∠OLN. b) What kind of triangle is ∆LON? Explain how you know. * a) 36° * b) Isosceles triangle 11. Sandy designed this logo for the jerseys worn by her softball team. She told the graphic artist that each interior angle of the regular decagon should measure 162°, based on this calculation: S(10) = 180°(10-1)/10 S(10)= 1620°/10 S(10) = 162° Identify the error she made and determine the correct angle. * The numerator of the formula for S(10) should be 180°(10 - 2); S(10) = 144°. 13. Martin is planning to build a hexagonal picnic table, as shown. a) Determine the angles at the ends of each piece of wood that Martin needs to cut for the seats. b) How would these angles change if Martin decided to make an octagonal table instead? * a) 60°, 120°, 120° * b) 67.5°, 67.5°, 112.5°, 112.5° 14. Three exterior angles of a convex pentagon measure 70°, 60°, and 90°. The other two exterior angles are congruent. Determine the measures of the interior angles of the pentagon. * 110°, 120°, 90°, 110°, 110° 15. Determine the sum of the measures of the indicated angles. * 360° 16. In each figure, the congruent sides form a regular polygon. Determine the values of a, b, c, and d. * a) ∠a=60°, ∠b=60°, ∠d=60°, ∠c=120° * b) ∠a=140°, ∠b=20°, ∠c=60°, ∠d=60° 17. Determine the sum of the measures of the indicated angles. * 720° ## Extending 20. A pentagon tile has two 90° angles. The other three angles are equal. Is it possible to create a tiling pattern using only this tile? Justify your answer. * Yes, e.g. A tiling pattern can be created by putting four 90° angles together or three 120° angles together. 21. Each interior angle of a regular polygon is five times as large as its corresponding exterior angle. What is the common name of this polygon? * Regular dodecagon ## Chapter 2 - Self Test: ### 1. Determine the values of a, b, and c. * a) a = 70°, b = 75°, c = 75° * b) a = 20°, b = 80°, c = 100° ### 2. Determine the value of x in the following diagrams. * a) x = 19° * b) x = 26° 4. Joyce is an artist who uses stained glass to create sun catchers, which are hung in windows. Joyce designed this sun catcher using triangles and regular hexagons. Determine the measure of the interior angles of each different polygon in her design. * Regular hexagons: six 120° angles; small triangles: three 60° angles; large triangles: one 120° angle and two 30° angles. 6. Determine the sum of the indicated angles. * 720° ## The Chapter Review: ### 2. * a) Name the pairs of corresponding angles. La, Le; Lb, Lg; Lc, Lf; Zd, Zh * b) Are any of the pairs you indentified in part a) equal? Explain. No. e.g., The lines are not parallel, so corresponding pairs cannot be equal. * c) How many pairs of supplementary angles can you see in the diagram? Name one pair. 8; e.g., La, ∠b * d) Are there any other pairs of equal angles? If so, name them. Yes; La, Ld; Lb, Lc; Le, ∠h; Lf, Lg ### 3. Determine the values of a and b. * ∠a = 35°, ∠b = 145° ### 4. Is AB parallel to CD? Explain how you know. * ∠a + ∠b = 180° (La and ∠b form a straight angle) * ∠a = 40° (Substitution and subtraction) * ∠c = 40° (Given) * ∠a = ∠c (Corresponding angles are equal) * AB || CD ### 5. Determine the values of a, b, and c. * a) a = 76°, b = 76°, c = 76° * b) a = 20°, b = 60°, c = 40° ### 7. Given: QR || ST Prove: ST = TR * ∠QRS = ∠RST (alternate interior angles) * ∠QRS = ∠TRS (given) * ∠RST = ∠TRS (transitive property) * TS = TR (isosceles triangle) ### 8. Determine the values of x, y, and z. * a) x = 40°, y = 95°, z = 45° * b) x = 68°, y = 112°, z = 40° ### 10. * a) Determine the sum of the measures of the interior angles of a 15-sided regular polygon. * b) Show that each exterior angle measures 24°. * a) 2340° * b) e.g., The sum of the 15 exterior angles is 360°, so each exterior angle is 360° ÷ 15 = 24°. ### 11. Given: ABCDE is a regular pentagon. Prove: AC || ED * ∠ABC = 108°, ∠BCD = 108°, ∠CDE = 108° (The angles in a regular pentagon are 108°. ) * ∠BCA + ∠BAC = 180° - 108° (The sum of the angles of △ABC is 180°.) * △ABC is isosceles with ∠BCA = ∠BAC. * 2∠BCA = 72° * ∠BCA = 36° * ∠ACD = ∠BCD - ∠BCA * ∠ACD = 108° - 36° * ∠ACD = 72° * ∠ACD = 72° and ∠CDE = 108° are supplementary interior angles on the same side of the transversal CD. * AC || ED