28.08.2021

WXYZ is a parallelogram. Find the measure of angle Z.

. 4

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Mathematics
Step-by-step answer
P Answered by PhD
Answer:
m∠X=55°;
m∠Z=55°;
m∠W=125°.

Explanation:
We know that consecutive angles of a parallelogram are supplementary.
As m∠Y=125°.
Hence, by the above property we have:
m∠Y+m∠X=180°;
125°+m∠X=180°;
Hence, m∠X=180°-125°;
⇒ m∠X=55°.
Also,
m∠Y+m∠Z=180°;
⇒ 125°+m∠Z=180°;
⇒ m∠Z=180°-125°;
⇒ m∠Z=55°.
Also, m∠Z+m∠W=180°;
⇒ 55°+m∠W=180°;
⇒ m∠W=180°-55°;
⇒ m∠W=125°.
Mathematics
Step-by-step answer
P Answered by PhD

angle W=80

angle WXZ=100

angle Z=80

and angle WYZ=100

Step-by-step explanation:

First we can find the measure of angle W since WZX is a triangle and we know the angles of a triangle =180

<1 + <3 + W =180

30 + 70 + W = 180

100 + W = 180

W = 80 degrees

Since this is a parallelogram

We know that <1 = <4 = 30 since they are alternate interior angles

And <2 = <3 = 70 since they are alternate interior angles

We know WXZ = <1 + <2  = 30 +70 = 100

We know WYZ = <3 + <4  = 70 +30 = 100

We also know that opposite angles in a parallelogram are equal so <W = <Z = 80

Mathematics
Step-by-step answer
P Answered by PhD

angle W=80

angle WXZ=100

angle Z=80

and angle WYZ=100

Step-by-step explanation:

First we can find the measure of angle W since WZX is a triangle and we know the angles of a triangle =180

<1 + <3 + W =180

30 + 70 + W = 180

100 + W = 180

W = 80 degrees

Since this is a parallelogram

We know that <1 = <4 = 30 since they are alternate interior angles

And <2 = <3 = 70 since they are alternate interior angles

We know WXZ = <1 + <2  = 30 +70 = 100

We know WYZ = <3 + <4  = 70 +30 = 100

We also know that opposite angles in a parallelogram are equal so <W = <Z = 80

Mathematics
Step-by-step answer
P Answered by PhD

W and Y = 91. X and Z = 89

Step-by-step explanation:

Those two angles will add to 180.

5a - 21 + 3a + 25 = 8a + 4

8a + 4 = 180

8a = 176

176 / 8 = 22 = a

Plug in a for an angle.

3(22) + 25 = 91

180 - 91 = 89

Mathematics
Step-by-step answer
P Answered by PhD

The correct angle measures are: m∠X = 55°

, m∠W = 125° and m∠Z = 55°

The measure of angle Y is given as:

\angle Y = 125^o

The opposite angles of a parallelogram are equal.

This means that, angles W and Y have equal measures

So, we have:

\angle W = \angle Y\angle W = 125^o

The adjacent angle of a parallelogram add up to 180 degrees.

So, we have:

\angle X = 180 - \angle Y\angle X = 180 - 125\angle X = 55

Angles X and Z are equal because they are opposite angles.

So, we have:

\angle Z = 55

Hence, the correct angle measures are: m∠X = 55°

, m∠W = 125° and m∠Z = 55°

Read more about parallelograms at:

link

Mathematics
Step-by-step answer
P Answered by PhD
Answer: the correct answer is:m∠X=55°;m∠Z=55°;m∠W=125°.Explanation:We know that consecutive angles o

Answer: the correct answer is:
m∠X=55°;
m∠Z=55°;
m∠W=125°.

Explanation:
We know that consecutive angles of a parallelogram are supplementary.
As m∠Y=125°.
Hence, by the above property we have:
m∠Y+m∠X=180°;
125°+m∠X=180°;
Hence, m∠X=180°-125°;
m∠X=55°.
Also,
m∠Y+m∠Z=180°;
125°+m∠Z=180°;
m∠Z=180°-125°;
m∠Z=55°.
Also, m∠Z+m∠W=180°;
55°+m∠W=180°;
m∠W=180°-55°;
m∠W=125°.

Mathematics
Step-by-step answer
P Answered by PhD

W and Y = 91. X and Z = 89

Step-by-step explanation:

Those two angles will add to 180.

5a - 21 + 3a + 25 = 8a + 4

8a + 4 = 180

8a = 176

176 / 8 = 22 = a

Plug in a for an angle.

3(22) + 25 = 91

180 - 91 = 89

Mathematics
Step-by-step answer
P Answered by Master

Hence, the correct answer is:

m∠X=55°m∠Z=55°m∠W=125°

Step-by-step explanation:

We know that consecutive angles of a parallelogram are supplementary.

As m∠Y=125°.

Hence, by the above property we have:

m∠Y+m∠X=180°

125°+m∠X=180°

Hence, m∠X=180°-125°

⇒ m∠X=55°

Also,

m∠Y+m∠Z=180°

⇒ 125°+m∠Z=180°

⇒ m∠Z=180°-125°

⇒ m∠Z=55°

Also, m∠Z+m∠W=180°

⇒ 55°+m∠W=180°

⇒ m∠W=180°-55°

⇒  m∠W=125°

Mathematics
Step-by-step answer
P Answered by PhD

The correct angle measures are: m∠X = 55°

, m∠W = 125° and m∠Z = 55°

The measure of angle Y is given as:

\angle Y = 125^o

The opposite angles of a parallelogram are equal.

This means that, angles W and Y have equal measures

So, we have:

\angle W = \angle Y\angle W = 125^o

The adjacent angle of a parallelogram add up to 180 degrees.

So, we have:

\angle X = 180 - \angle Y\angle X = 180 - 125\angle X = 55

Angles X and Z are equal because they are opposite angles.

So, we have:

\angle Z = 55

Hence, the correct angle measures are: m∠X = 55°

, m∠W = 125° and m∠Z = 55°

Read more about parallelograms at:

link

Mathematics
Step-by-step answer
P Answered by Master

length of segment YZ is 8 cm

Step-by-step explanation:

given data

AB = 16 cm

DA = 3\sqrt{2} cm

AB and DA form interior angle  =  45-degre

WX ≠ YZ

WX = 16 cm

to find out

length of segment YZ

solution

area of △ABD is  the same as the area of △BCD

and

area of △ABD is express as

area of △ABD = AB × AD × sin(45) ÷ 2    ............1

put here value

area of △ABD = 16 × 3√2 × sin(45) ÷ 2

area of △ABD = 24

and

area of the parallelogram is

area of the parallelogram = 24 × 2

area of the parallelogram = 48

so

now we will consider here YZ = x

and Since ZY XW is isosceles trapezoid

so here we can say that

WM = ZM = (16 - x)  ÷ 2   .......................2

so area of  trapezoid will be

area of  trapezoid = \frac{ZY + WX }{2}  \times ZM         .......................3

area of  trapezoid = \frac{x+16}{2} \times \frac{16 - x}{2}    

48 = \frac{x+16}{2} \times \frac{16 - x}{2}  

solve it we get

x = 8

so length of segment YZ is 8 cm


In parallelogram ABCD, AB = 16 cm, DA = 3 cm, and sides AB and DA form a 45-degree interior angle. I

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