Question

If a 5th pt is located on the diagram so that m 11 years ago

Answer 1

First, you need to solve for x.
What do you know abnout angles ABD and ABC?

Answer 2

there supplementary

Answer 3

Good.
What do you know about supplementary angles?

Answer 4

=180

Answer 5

They add to 180.
Good.

Add the angles and set it equal to 180.
Then solve for x.

Answer 6

x=49

Answer 7

Good.
If x = 49, then what is \(m\angle EBC = \sqrt{x} +83\)
Plug in 49 for x.

Answer 8

m<EBC=90

Answer 9

Correct.

Answer 10

Now what are the measures of the two angles we already dealt with, angle ABD and angle ABC?
Insert x = 49 into each expression with x.

Answer 11

a. is line AB perp to line DC?
~ SO WOULD IT BE YES, BY THIS THEORM:
IF 2 PT ARE =DIST FROM THE ENDPTS OF A SEG, THEN THE 2 PTS DETERMINE THE PERP BIS. OF THAT ANGLE OR NO

Answer 12

We don't know anything about distances. Nothing in this problem deals with distances. All we have is angle measures.

Answer 13

We have
m<ABD = 2x - 8
m<ABC = x + 41
Can you replace x with 49 in the two measures above
and find the measures of angles ABD and ABC?

Answer 14

M<ABD=90
M<ABC=90

Answer 15

Correct.
Point E is also on a ray that makes an angle of 90 degrees.

Answer 16

Let's answer the first question.

Answer 17

Is line AB perpendicular to line DC?

Answer 18

yes, bcuz 90 degrees

Answer 19

Correct.

Answer 20

Now let's look at the second question.

Answer 21

so by what theorem can i justify my answer with?

Answer 22

It's not a theorem. It's the definition of perpendicular lines.

Answer 23

ok so then #b would it have to do with perpendicular too