New SAT Math Workbook

Additional properties would be needed to make it a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ary to ∠CEF. ∠ AEC = 80° 3. (E) The exterior angle is equal to the sum of the two remote interior angles. 4 x = 100 x = 25 Angle A = 3x = 75° 4. (D) The other base angle is also x. These two base angles add to 2x. The remaining degrees of the triangle, or 180 – 2x, are in the vertex angle. (E) ∠1 = ∠3 ∠2 + ∠3 = 180° ∠2 = 50° 5. 4. (C) Since ∠BEG and ∠EGD add to 180°, halves of these angles must add to 90°. Triangle EFG contains 180°, leaving 90° for ∠EFG. (C) ∠A = ∠C 4 x − 30 = 2 x + 10 2 x = 40 x = 20 5. ∠ A and ∠ C are each 50°, leaving 80° for ∠ B. ∠1 = ∠3 ∠2 = ∠4 ∠1 + ∠2 = ∠3 + ∠4 But ∠3 + ∠4 = 180°. Therefore, ∠1 + ∠2 = 180° www.petersons.com Geometry 227 Exercise 7 1. 2. (C) A hexagon has 6 sides. Sum = (n – 2) 180 = 4(180) = 720 (D) Opposite sides of a parallelogram are congruent, so AB = CD. x + 4 = 2 x − 16 20 = x AD = BC = x − 6 = 14 Exercise 8 1. (C) Tangent segments drawn to a circle from the same external point are congruent. If CE = 5, then CF = 5, leaving 7 for BF. Therefore BD is also 7. If AE = 2, then AD = 2. BD + DA = BA = 9 2. (D) Angle O is a central angle equal to its arc, 40°. This leaves 140° for the other two angles. Since the triangle is isosceles, because the legs are equal radii, each angle is 70°. (E) The remaining arc is 120°. The inscribed 1 angle x is its intercepted arc. 2 3. (B) AB = CD x + 8 = 4x − 4 12 = 3x 3. AB = 12 x=4 BC = 12 CD = 12 4. (A) If all sides are congruent, it must be a rhombus. Additional properties would be needed to make it a square. 4. 5. (B) A rhombus has 4 sides. Sum = (n – 2) 180 = 2(180) = 360 (C) Rectangles and rhombuses are both types of parallelograms but do not share the same special properties. A square is both a rectangle and a rhombus with added properties. 5. 1 ( 40° + AC ) 2 100° = 40° + AC 60° = AC 50° = (D) An angle outside the circle is the 2 difference of its intercepted arcs. 1 www.petersons.com 228 Chapter 13 Exe...
View Full Document

Ask a homework question - tutors are online