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# Polygons a the sum of the measures of the angles of a

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Unformatted text preview: ior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Angle 1 = 140° E. If two angles of one triangle are congruent to two angles of a second triangle, the third angles are congruent. Angle A will be congruent to angle R. www.petersons.com Geometry 213 Exercise 6 Work out each problem. Circle the letter that appears before your answer. 1. The angles of a triangle are in the ratio 1 : 5 : 6. This triangle is (A) acute (B) obtuse (C) isosceles (D) right (E) equilateral If the vertex angle of an isosceles triangle is 50°, find the number of degrees in one of the base angles. (A) 50 (B) 130 (C) 60 (D) 65 (E) 55 In triangle ABC, angle A is three times as large as angle B. The exterior angle at C is 100°. Find the number of degrees in angle A. (A) 60 (B) 80 (C) 20 (D) 25 (E) 75 4. If a base angle of an isosceles triangle is represented by x°, represent the number of degrees in the vertex angle. (A) 180 – x (B) x – 180 (C) 2x – 180 (D) 180 – 2x (E) 90 – 2x In triangle ABC, AB = BC . If angle A = (4x – 30)° and angle C = (2x + 10)°, find the number of degrees in angle B. (A) 20 (B) 40 (C) 50 (D) 100 (E) 80 2. 5. 3. www.petersons.com 214 Chapter 13 7. POLYGONS A. The sum of the measures of the angles of a polygon of n sides is (n – 2)180°. Since ABCDE has 5 sides, angle A + angle B + angle C + angle D + angle E = (5 – 2)180° = 3(180)° = 540° B. Properties of a parallelogram a) b) c) d) e) Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other C. Properties of a rectangle a) b) c) All 5 properties of a parallelogram All angles are right angles Diagonals are congruent D. Properties of a rhombus a) b) c) d) All 5 properties of a parallelogram All sides are congruent Diagonals are perpendicular to each other Diagonals bisect the angles E. Properties of a square a) b) c) All 5 parallelogram properties Two additional rectangle properties Three additional rhombus pro...
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## This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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