Answers: 33. Angle R is 68 degrees 35. The fraction 21/2 or the decimal 10.5 36. Triangle ACG 37. Segment AB 38. The values are x = 6; y = 2 40. The value of x is x = 29 41. C) 108 degrees 42. The value of x is x = 70 43. The segment WY is 24 units long ------------------------------------------------------ Work Shown: Problem 33) RS = ST, means that the vertex angle is at angle S Angle S = 44 Angle R = x, angle T = x are the base angles R+S+T = 180 x+44+x = 180 2x+44 = 180 2x+44-44 = 180-44 2x = 136 2x/2 = 136/2 x = 68 So angle R is 68 degrees ----------------- Problem 35) Angle A = angle H Angle B = angle I Angle C = angle J A = 97 B = 4x+4 C = J = 37 A+B+C = 180 97+4x+4+37 = 180 4x+138 = 180 4x+138-138 = 180-138 4x = 42 4x/4 = 42/4 x = 21/2 x = 10.5 ----------------- Problem 36) GD is the median of triangle ACG. It stretches from the vertex G to point D. Point D is the midpoint of segment AC ----------------- Problem 37) Segment AB is an altitude of triangle ACG. It is perpendicular to line CG (extend out segment CG) and it goes through vertex A. ----------------- Problem 38) triangle LMN = triangle PQR LM = PQ MN = QR LN = PR Since LM = PQ, we can say 2x+3 = 5x-15. Let's solve for x 2x+3 = 5x-15 2x-5x = -15-3 -3x = -18 x = -18/(-3) x = 6 Similarly, MN = QR, so 9 = 3y+3 Solve for y 9 = 3y+3 3y+3 = 9 3y+3-3 = 9-3 3y = 6 3y/3 = 6/3 y = 2 ----------------- Problem 40) The remote interior angles (2x and 21) add up to the exterior angle (3x-8) 2x+21 = 3x-8 2x-3x = -8-21 -x = -29 x = 29 ----------------- Problem 41) For any quadrilateral, the four angles always add to 360 degrees J+K+L+M = 360 3x+45+2x+45 = 360 5x+90 = 360 5x+90-90 = 360-90 5x = 270 5x/5 = 270/5 x = 54 Use this to find L L = 2x L = 2*54 L = 108 ----------------- Problem 42) The adjacent or consecutive angles are supplementary. They add to 180 degrees K+N = 180 2x+40 = 180 2x+40-40 = 180-40 2x = 140 2x/2 = 140/2 x = 70 ----------------- Problem 43) All sides of the rhombus are congruent, so WX = WZ. Triangle WPZ is a right triangle (right angle at point P). Use the pythagorean theorem to find PW a^2+b^2 = c^2 (PW)^2+(PZ)^2 = (WZ)^2 (PW)^2+256 = 400 (PW)^2+256-256 = 400-256 (PW)^2 = 144 PW = sqrt(144) PW = 12 WY = 2*PW WY = 2*12 WY = 24