Question

In the diagram below, P is circumscribed about quadrilateral ABCD. What is the value of x?

https://docs.google.com/document/d/1y48Rs5w4YW_IwOmc4tC7mher6cRicCPXzh5TKR71e3M/edit?usp=sharing

Answer 1

How do I get to your doc?

Answer 2

it should be a link if you click it...is it not working?

Answer 3

It says I need permission.

Answer 4

@YourBoyDusty
You have to set the permission to "anyone with a link" or else we don't see the doc.

Answer 5

okay try it now

Answer 6

Ok, I'm in.

Answer 7

You need to know this:
Opposite angles of an inscribed quadrilateral are supplementary.

Answer 8

so B would be 115 and C would be 70?

Answer 9

You are missing two things.
First, you need to deal with opposite angles.
Second, they are supplementary, not congruent.

Answer 10

Once again:
In an inscribed quadrilateral, opposite angles are supplementary.
1. Can you name two pairs of opposite angles in your quadrilateral?

Answer 11

yes < A and <c ...right?

Answer 12

Good.

A and C
B and D
are two pairs of opposite angles.

We need A and C since one has x in it, and the other one has a measure.
B and D will not help since there is no x in their measures.

Answer 13

im sorry geometry does not like to make things easy for me...and math is hard for me...

Answer 14

Angles A and C are supplementary.
What does that mean?

Answer 15

We're doing it one step at a time.

Answer 16

they intersect

Answer 17

oh...either of two angles whose sum is 180°.

Answer 18

The second answer is correct.
Two angles are supplementary angles if the sum of their measures is 180 degrees.
That means that the sum of the measures of angles A and C is 180 degrees

We have a measure for angle A and an expression for the measure of angle C.
We add the measures and set the measure equal to 180 degrees.

Answer 19

\(m\angle A + m \angle D = 180\)

\(70 + x + 10 = 180\)

Do you understand how we got the equation?

Answer 20

i think so...

Since 70+115=180
then you plug the numbers in to get an equation. Right?

Answer 21

wait...no that equalled 185... but the sum of two angles equals 180?

Answer 22

No.
70 + 115 = 185, but that has nothing to do with this.

Answer 23

We are not using the 115-deg angle at all.
We are only using the opposite angles A and C.

Answer 24

Angle A measures 70 deg.
Angle C measures x + 10.
We know that angles and C are supplementary.
That means we know that the sum of the measures of angles A and C is 180.

Answer 25

okay i follow you...