Chapter 6 Review Polygons.

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Presentation transcript:

Chapter 6 Review Polygons

6-1 Angles of Polygons # Sides: angle x n=180(n – 2) YOU MUST REMEMBER THESE EQUATIONS # Sides: angle x n=180(n – 2)

Example #1 A decorative window is designed to have the shape of a regular octagon. Find the sum of the measures of the interior angles and the exterior angles of the octagon. Find the measure of each interior angle and each exterior angle.

Example #2 The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon.

Example #3 Find the measure of each interior angle.

Example #4 Find the value of x.

You must know…

Example #5 Quadrilateral RSTU is a parallelogram. Find mURT, mRST, and y.

Example #6 ABCD is a parallelogram. Find mBDC.

Example #7 Determine whether the quadrilateral is a parallelogram. Justify your answer.

YOU NEED TO KNOW

Example #8 Find x so that the quadrilateral is a parallelogram

YOU NEED TO KNOW

Example #9 Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x.

Example #10 Quadrilateral EFGH is a rectangle. If FH = 5x + 4 and GE = 7x – 6, find x.

Example #11 Quadrilateral LMNP is a rectangle. Find x.

Example #12 Quadrilateral EFGH is a rectangle. Find x.

Example #13 Use rhombus LMNP to find mPNL if mMLP = 64.

Example #14 DEFG is an isosceles trapezoid with median MN. Find DG if EF = 20 and MN = 30.

Example #15 DEFG is an isosceles trapezoid with median MN. Find m1, m2, m3, and m4 if m1 = 3x + 5 and m3 = 6x – 5.

Example #16 WXYZ is an isosceles trapezoid with median JK. Find XY if JK = 18 and WZ = 25.

Answers: #1. Int: 180(8-2)= 1080 ext: 360 1080/8= 135 360/8= 45 1080/8= 135 360/8= 45 #2. 144n = 180(n-2) n= 10 #3. 180(4-2) = 360 360= 11x+4+5x+11x+4+5x x = 11 angle S and U = 125 angle R and t = 55

#4. 180(4-2) = 360 360 = 10x+6x+6x+3x-15 x= 15 #5. angle URT = 40 angle RST = 122 y = 6 #6. angle BDC = 54

#7. Yes, because in a parallelogram both sets of opposite sides are congruent. #8. 4x-1=3(x+2) x=7 #9. 6x+4=7x-4 x=8 #10. 5x+4=7x-6 x=5

#11. 5x+8+3x+2=90 x=10 #12. x2+2=14x-47 x2-14x+49=0 x=7 #13. angle PNL = 32 #14. 30=1/2 (DG + 20) DG = 40

#15. 3x+5+6x-5=180 x=20 angle 1 and 2 = 65 angle 3 and 4 = 115 #16. 18 = ½ (XY + 25) XY = 11