Angles in Polygons
What is the sum of the interior angles in a 15-gon?
2,340°
Page 518 #11
WXYZ is a parallelogram
m<Y = 61°
The pair that is formed by the lines that are not congruent.
Page 518 #15
x = 4, y = 4
Name the two properties unique to a rectangle.
Only acceptable answers:
1. Diagonals are congruent
2. All four angles are right angles or are equal.
If a quadrilateral has two pairs of congruent base angles, is it automatically a trapezoid?
Yes. In fact, it's an isosceles trapezoid.
Rhombus, square, kite
A pentagon (5 sides) angles of 15°, 75°, 150°, 200°, and x°. Find the value of x.
100
Page 519 #27
m<HGF = 130°
page 538 #29
It's a parallelogram. We know this because both pairs of opposite sides are congruent.
x = 13, y = 2
A kite has one angle of 60° and another angle of 110°. What are the two missing angles? (Think about the properties of a kite)
Both are 95° because one pair of opposite angles in a kite are congruent.
True or false: if the diagonals of a quadrilateral are congruent, the quadrilateral is automatically a square.
False; it could be a rectangle or an isosceles trapezoid.
Name 2 ways to prove that a certain quadrilateral is a parallelogram
Possible Answers
1. Both pairs of opposite sides are parallel
2. Both pairs of opposite sides are congruent
3. Both pairs of opposite angles are congruent
4. Diagonals bisect each other
5. One pair of opposite sides is both congruent AND parallel.
For any rhombus JKLM, decide whether the statement is always true or sometimes true.
JL is perpendicular to KM
Always true
In a rhombus, the diagonals are always perpendicular to each other.
Is JKLM on page 555 #20 automatically a square?
No. It has four right angles, but it has no other property that demands it to be a square. The diagonals of all parallelograms bisect each other.
The floor of a greenhouse is shaped like a regular decagon (10 sides). Find the measure of one interior angle.
144°
Page 538 #38
m<SRT = 56°
Page 547 #27
Find the value of x
x = 2.3