Question

Need help with 11 through 18 help anyone http://www.ocs.cnyric.org/webpages/jmelfi/files/GE09S3P1.PDF

Answer 1

For number 14, you have a line AD which is parallel to BC, right, since it's a parallelogram?

Answer 2

yes I got that

Answer 3

The line AC is a transverse line to this set of parallel lines, so x and angle CAD, which measures 46 degrees, are congruent.
Thus, x = 46 degrees.

Answer 4

Because x and angle CAD are alternate interior angles.

Answer 5

Then angle BCD measures 44 + 46 = 90 degrees, making it a right angle.
This makes angle BAD a right angle as well.

All quadrilaterals have interior angles that sum up to 360 degrees, and in parallelograms, opposite angles are congruent, so angle ABC is a right angle, as well as angle ADC.

It's a rectangle.

Answer 6

because all its interior angles are right angles. We know nothing about the lengths of the sides or the angle made by its diagonals, so we cannot say it's a square.

Answer 7

Is it a rectangle then

Answer 8

Yes, and that's the best we can say about it.

Answer 9

okay so what would X be

Answer 10

X is alternate interior to the angle measuring 46 degrees, and therefore has the same measure.

Answer 11

oh ok so can we do number 11

Answer 12

Right...
For number 11, you can get the value of x immediately.
Ever heard of vertical angles?

Answer 13

yes isnt it V shape

Answer 14

What's the vertical angle to the angle measuring x-degrees?

Answer 15

Here's an example of a pair of vertical angles:

Answer 16

So clearly, x and the angle measuring 85 degrees are vertical angles.
Vertical angles are always congruent, so
x = 85 degrees.

Answer 17

so the shape would be a square

Answer 18

then you would subtract 180- 85 then get 95 to be y

Answer 19

No. Remember that for something to be a square (or a rhombus, for that matter), the diagonals must be perpendicular. Are they?

Answer 20

no

Answer 21

would it be a parallelogram

Answer 22

No. Let's take a piece of that square, shall we?

Answer 23

so it is a square

Answer 24

THIS is the angle that measures 95 degrees.

Answer 25

They are ALL parallelograms.

Answer 26

Again, for it to be a square, the diagonals MUST be perpendicular, and they're not, as you said.

Answer 27

oh so I was right it is 95

Answer 28

That angle is 95, but that is not y.
In particular, since this is an isosceles triangle, then that other angle is also congruent to y

Answer 29

So, knowing that all triangles have interior angles summing up to 180, you get
95 + y + y = 180
2y = 85
y = 42.5

Answer 30

oh ok

Answer 31

Also, if you look at it, one of the angles of the parallelogram is right, but it is not a square, therefore, it must be a...?

Answer 32

parallelogram

Answer 33

no rectangle

Answer 34

Yeah, it's a rectangle.

Answer 35

okay and number 15

Answer 36

All sides are congruent. It must at least be a...?

Answer 37

rectangle

Answer 38

Rhombus, it must least be a rhombus.
Now, what we know about rhombuses, their diagonals bisect their interior angles...
In particular, that 55 degrees is just half of that corner angle.

Also, x is alternate interior to that 55-degree angle, so x is also 55 degrees.

Now, we know one corner, as well as its opposite, measure twice 55, and that's 110 degrees apiece.

Quadrilaterals have interior angles that measure 360 degrees, so y, as well as its opposite which also measures y degrees, so you get
110 + 110 + y + y = 360
2y + 220 = 360
2y = 140
y = 70

Answer 39

Now, it's a rhombus, but the corners are not right angles, so it's not a square, it's just a rhombus.

Answer 40

oh ok

Answer 41

thank you so much i get it

Answer 42

No problem
Terence out :)

Answer 43

ok