All categories

2 years ago

In Quadrilateral ABCD , AB ∥ CD, and m∠2=35°.

Mathematics

2 answers:

Marianna [84]2 years ago

4 0

Angle 2 and 5 are alternate interior angle and they are congruent. That means that m <5= 35°.

scZoUnD [109]2 years ago

4 0

we know that

Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal. Alternate interior angles are congruent

In this problem

the parallel lines are AB and CD

the transversal line is BD

then

m∠5=m∠2 ------> by alternate interior angles

m∠5= $35\°$

therefore

the answer is

m∠5= $35\°$

You might be interested in

12 catsate 40 pounds of cat food.At this rate, how many pounds of cat food would 48 cats eat?

max2010maxim [7]

The answer is 160, multiply 12 by 4 to get 48 cats. 40 multiplied by 4 = 160.
If that makes since.

Hope this helps

3 0

2 years ago

In the diagram, transversal t cuts across the parallel lines a and b. Match the pairs of angles with the relationship that shows

charle [14.2K]

we know that

case a) alternate exterior angles

m∠2=m∠7 --------> by alternate exterior angles

m∠1=m∠8 --------> by alternate exterior angles

case b) alternate interior angles

m∠3=m∠6 --------> by alternate interior angles

m∠5=m∠4 --------> by alternate interior angles

case c) corresponding angles

m∠1=m∠5 --------> by corresponding angles

m∠3=m∠7 --------> by corresponding angles

m∠2=m∠6 --------> by corresponding angles

m∠4=m∠8 --------> by corresponding angles

case d) vertical angles

m∠1=m∠4 --------> by vertical angles

m∠2=m∠3 --------> by vertical angles

m∠5=m∠8 --------> by vertical angles

m∠6=m∠7 --------> by vertical angles

therefore

the answer in the attached figure

5 0

2 years ago

Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 + y2.

vekshin1

$x^2+y^2+z^2=100z\iff x^2+y^2+(z-50)^2=50^2$

The surface of interest can be parameterized by

$\mathbf r(u,v)=\begin{cases}x(u,v)=50\cos u\sin v\\y(u,v)=50\sin u\sin v\\z(u,v)=50(\cos v+1)\end{cases}$

with $0\le u\le2\pi$ and $0\le v\le\arccos\dfrac{49}{50}$ .

The area of the surface $S$ is given by the surface integral

$\displaystyle\iint_S\mathrm dA=\iint_T\left\|\mathbf r_u\times\mathbf r_v\right\|\,\mathrm du\,\mathrm dv$

We have

$\|\mathbf r_u\times\mathbf r_v\|=50^2\sin v$

so the area is given by the double integral

$\displaystyle50^2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\arccos(49/50)}\sin v\,\mathrm dv\,\mathrm du=100\pi$

6 0

2 years ago

Sixty-five campers arrive. Nine go home early. If 8 people sleep in 1 tent, how many tents will the campers need?

allsm [11]

65-9=56

56 divided by 8 is 7

So they will need 7 tents

4 0

2 years ago

Mia had $32. Then she started to receive $5 a week as an allowance. She plans to save all of her money for a bicycle and draws a

kompoz [17]

Only 4,52 would be on the graph.
If she stated at week 0 with 32 dollars it would be:
0, 32
1, 37
2, 42
3, 47
4, 52
5, 57
6, 62
7, 67
and so on.