Quadrilateral bcde is inscribed inside a circle as shown below. write a proof showing that angles c and e are supplementary. circle a is shown with an inscribed quadrilateral labeled bcde.

The sum of angle C and E is 180°. So, C and E are supplementary angles.

Step-by-step explanation:

Given information: Quadrilateral BCDE is inscribed inside a circle.

To prove : angles C and E are supplementary, i.e., ∠C+∠E=180°.

Proof:

BCDE is a cyclic quadrilateral.

According to central angles theorem, the inscribed angle on a circle is half of its central angle.

By using Central angle theorem

                .... (1)

             ..... (2)

The complete central angles of a circle is 360°.

Using (1) and (2), we get

Divide both sides by 2.

The sum of angle C and E is 180°. So, C and E are supplementary angles.

Hence proved.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

1,8,15,22,29,36,43,50

step-by-step explanation: