Angles of Polygons
Properties of Parallelograms
More Parallelograms!
Rectangles, Rhombi, & Squares
Trapezoids & Kites
100
The sum of the measures of the interior angles of a polygon is 1800°. How many sides does the polygon have?
12 sides; It is a dodecagon.
100
In ▱STUV, segment ST = 29, and VU = 2x+5. Find the value of x.
x = 12
100
Find the values of x and y that make the quadrilateral a parallelogram.
x = 120°, y = 60°
100
WXYZ is a rhombus. Find m∠WVX.
90°
100
Find m∠C in the kite shown.
m∠C = 115°
200
Find the value of x in the diagram.
105°
200
In parallelogram PQRS, m∠Q is 112°. What is half of m∠R?
34°
200
For what value of x is quadrilateral CDEF a parallelogram?
x = 14
200
If ABCD is a square, name the angle(s) congruent to ∠A and the segment(s) congruent to segment AB.
∠A≅∠B≅∠C≅∠D
and
AB≅BC≅CD≅AD
200
ABCD is an isosceles trapezoid, and m∠D = 42°. Find m∠A, m∠B, and m∠C.
m∠B = 138°, m∠C = 138°, m∠D = 42°
300
Find the value of x in the diagram.
x = 57
300
Find the values of x and y.
x = 27, y = 7
300
Find m∠ADB if m∠ABC = 78° and m∠CBD = 41° in parallelogram ABCD.
m∠ADB = 41°
300
Write always, sometimes or never true for each statement:
a) “A rectangle is a rhombus.”
b) “A square is a rectangle.”
c) “A trapezoid is a parallelogram.”
a)Sometimes
b)Always
c)Never
300
In the diagram, MN is the midsegment of trapezoid PQRS. Find MN.
16.2 inches
400
The measures of the interior angles of a quadrilateral are x°, 3x°, 5x°, and 7x°.
Find the measures of all the interior angles.
22.5°, 67.5°, 112.5°, 157.5°
400
In parallelogram PQRS, m∠P is four times m∠Q. Find m∠P.
144°
400
For what values of x and y is quadrilateral STUV a parallelogram?
x = 9, y = 21
400
In rectangle ABCD, AC = 7x − 15 and BD = 2x + 25. Find the lengths of the diagonals of ABCD.
AC = BD = 41 units
400
Find the length of segment AD in Kite ABCD if AC = 6 and ED = 4.
AD = 5
500
A polygon is shown.
a)Is the polygon regular? Explain your reasoning.
b)Find the measures of ∠B, ∠D, ∠E, and ∠G.
a) The polygon is not equiangular, so it is not regular.
b) m∠B = m∠D = m∠E = m∠G = 125°
500
In ▱STUV, diagonal VT = 4x-5 and segment WS = x+11. Find the value of x.
x = 13.5
500
Find the lengths of the sides of a parallelogram where the longer sides equal 3x and the shorter sides equal x + 1 and the perimeter is 18.
500
Find m∠ABC and m∠ACB in rhombus ABCD.
m∠ABC = 58°, m∠ACB = 61°
500
Determine which pairs of segments or angles must be congruent so that you can prove that ABCD is an isosceles trapezoid. Explain your reasoning.
∠A ≅ ∠D, or ∠B ≅ ∠C - base angles need to be congruent.
or
AB ≅ CD - nonparallel sides (legs) are congruent