Interior and exterior polygons
What is the interior angle sum formula?
S=(n-2) x 180
If you have a parallelogram ABCD (Draw the shape out)
D= 68 degrees AB= 15 BC=8
What do these equal
AD= DC= m C= m B= m A=
AD=8 DC=15 m C=112 degrees m B=68 degrees m A=112 degrees
What is the main property of a rectangle?
All four angles are right angles!
Given a rhombus with the sides EF=23 and DF=40
SEE SLIDE 3 FOR PICTURE
Find , GF, HF, GH, GE
GF=23, HF=20, GH=11.4, GE=22.8
Use Pythagorean theorem to solve
If this is a trapezoid
m C=
m D=
SEE SLIDE 8 FOR PICTURE
m C=149
m D=118
Consecutive sides are supplementary!!
Find the sum of the measures of the interior angles of a 21-gon.
Formula : (21-2) x 180
=3420
What are the properties of a parallelogram?
Both pairs of opposite sides are equal
Opposite sides and angles are congruent
Consecutive angles are supplementary
Diagonals bisect each other
If you are given a rectangle PQRS and PS=10 and PQ=24 what is the sum of the rectangle
68
If FGHI is a square, solve for x
SEE SLIDE 4 FOR PICTURE
X=6
Knowing that each angle in a square is 90 degrees you can assume that when bisected they will each be 45 degrees, so you can multiply the 7x+3 by 2 to and set that equal to 90 degrees.
If ABCD is an isosceles trapezoid, find each missing angle
m A= m B= m C= m D=
SEE SLIDE 9 FOR PICTURE
m A= 127 degrees m B= 127degreed m C= 53degrees m D=53 degrees
Set your 2 given angles equal to each other, solve for x then substitute for each angle
Find the measure of the interior angle of a REGULAR 18-gon
2880/18 = 160 degrees
If LM and PN are parallel in a parallelogram and LM= 9x-25 and PN=5x+7
solve for x
9x-25=5x+7
4x=32
x=8
You are given a rectangle CDEF and CD=3x+5 and EF=7x-39 (these are across from each other)
Find EF
EF= 38
If STUV is a square find the missing measures
VU= SU= TV= SW=
SEE SLIDE 6 FOR PICTURE
VU=15 SU=21.2 TV=21.2 SW=10.6
Use Pythagorean theorem to find your missing sides!
If the quadrilateral is a kite, find the missing values
m PTQ= m PQT= m QRT=
SEE SLIDE 10 FOR PICTURE
m PTQ= 90 degrees m PQT= 53 degrees m 37 degrees
(one pair of diagonals are equal)
What is the measure of each exterior angle of a regular hexagon?
360/6=60 degrees
If you have a parallelogram ABCD and A and C are opposite interior angles find the measure B
A= (6x-15) degrees
C= (4x+11) degrees
measure B = 97 degrees
See slide 1 for picture
find these lengths
QR, SR, SQ, PR, QT
QR=10, SR=24, SQ=26, PR=26, QT=13
Find PQ
SEE SLIDE 7 FOR PICTURE
PQ=76
ALL 4 SIDES ARE EQUAL
set your known sides equal
Solve for X
SEE SLIDE 11 FOR PICTURE
x=9
remember that 1 pair of opposite sides are equal so in this instant set your 2 givens equal!
If you have a hexagon with these following interior angle measures:129, 115, 124, 117, 112, 123.
What does each measures exterior sum and what do they all add up to?
51, 65, 56, 63, 68, 57
These angles all add up to 360 degrees.
If you have a parallelogram PQRS and P and Q are consecutive interior angles what is m R
P=(3x+5) degrees
Q=(8x-12) degrees
m R = 56 degrees
SEE SLIDE 2 FOR PICTURE
m XZW= 57 degrees
The way to solve this problem:
Given m XZY= x+20 and m ZXY= 5x-8
these are consecutive interior angles which means they are on the same side, therefore you would set them equal to 180 to find your x and then substitute that number to find XZW!
If STUV is a square with SW=2x + 13 and WU=8x-41 find VT
SEE SLIDE 5 FOR PICTURE
VT = 62
Find m FGJ
SEE SLIDE 12 FOR PICTURE(LAST SLIDE)
Set your 2 givens equal then substitute and subtract from 360!