1. ## geometry with angles

http://i4.photobucket.com/albums/y10...us/angles2.jpg

Okay:

a. since triangleABC is equilateral, write a eqaution showing a relationship betwen its angles.

b. Audrey rotated triangleABC around point A to form triangle AB'C'. She told her teammate Maria, " I think the two angles at A are equal." MAria did not know which angles she was referring to. How many angles can you find at A? Are there more than 3?

c. Maria asked Audrey to be more specific. She explained, "One of my angles is (anglesign) BAB'." at the same time, she marked her two angles with the same marking to indicate they have the same measure. Name her other angle. Be sure to use three letters so there is no confusion about which angle you mean.

a. Two angles that have a sum of 90 degrees are called complementary angles. Since angle ABD is a right angle, angles ABC and CBD are complementary. IF angle CBD= 76 degrees, what is angle ABC? Show how you got your answer.

b. Another special angle is 180 degrees . if the sum of the measures of two angles is 180 degrees, they're called supplementary angles. in the diagram, LMN is a straight angle. if angle LMP=62 degrees, what is angle PMN?

(USE THE intersecting diagram)
If x=23 degrees, find angle AEC, angle DEB, and angle CEB. show your work.

which angle is congruent to angle AED?

Angles AED and CEB are vertical angles. find another pair of vertical angles in the diagram.

2. Originally Posted by peachgal
http://i4.photobucket.com/albums/y10...us/angles2.jpg

Okay:

a. since triangleABC is equilateral, write a eqaution showing a relationship betwen its angles.

b. Audrey rotated triangleABC around point A to form triangle AB'C'. She told her teammate Maria, " I think the two angles at A are equal." MAria did not know which angles she was referring to. How many angles can you find at A? Are there more than 3?

c. Maria asked Audrey to be more specific. She explained, "One of my angles is (anglesign) BAB'." at the same time, she marked her two angles with the same marking to indicate they have the same measure. Name her other angle. Be sure to use three letters so there is no confusion about which angle you mean.

a. Two angles that have a sum of 90 degrees are called complementary angles. Since angle ABD is a right angle, angles ABC and CBD are complementary. IF angle CBD= 76 degrees, what is angle ABC? Show how you got your answer.

b. Another special angle is 180 degrees . if the sum of the measures of two angles is 180 degrees, they're called supplementary angles. in the diagram, LMN is a straight angle. if angle LMP=62 degrees, what is angle PMN?

(USE THE intersecting diagram)
If x=23 degrees, find angle AEC, angle DEB, and angle CEB. show your work.

which angle is congruent to angle AED?

Angles AED and CEB are vertical angles. find another pair of vertical angles in the diagram.
a) Since the triangle is equilateral, all angles of the triangle are equal.

b) I got 6: BAC', BAC, BAB', B'AC, B'AB, and CAC'.

c) It's CAC'. Now, can you tell me why?

====================================
a) The sum of the two angles is 90. So...
ABC + CBD = 90
ABC + 76 = 90
ABC + 76 - 76 = 90 - 76
ABC = 14

b)
LMP + PMN = 180
62 + PMN = 180
-62 + 62 + PMN = -62 + 180
PMN = 168
===================================
x = 23
CEB = x = 23 since x (that is, angle AED) and CEB are vertical angles.

AEC + x = 180 since AEC and AED are supplementary. Thus AEC = 157.

DEB = AEC = 157 since they are vertical angles. (Or you could say that DEB and AED are supplementary.)

-Dan

3. Originally Posted by topsquark
a) Since the triangle is equilateral, all angles of the triangle are equal.

b) I got 6: BAC', BAC, BAB', B'AC, B'AB, and CAC'.

c) It's CAC'. Now, can you tell me why?

====================================
a) The sum of the two angles is 90. So...
ABC + CBD = 90
ABC + 76 = 90
ABC + 76 - 76 = 90 - 76
ABC = 14

b)
LMP + PMN = 180
62 + PMN = 180
-62 + 62 + PMN = -62 + 180
PMN = 168
===================================
x = 23
CEB = x = 23 since x (that is, angle AED) and CEB are vertical angles.

AEC + x = 180 since AEC and AED are supplementary. Thus AEC = 157.

DEB = AEC = 157 since they are vertical angles. (Or you could say that DEB and AED are supplementary.)

-Dan
Thanks but I still need help with the rest!

4. Originally Posted by peachgal
Thanks but I still need help with the rest!
The rest of what? I think I answered all the questions you asked? What didn't I answer?

-Dan

5. Originally Posted by topsquark
The rest of what? I think I answered all the questions you asked? What didn't I answer?

-Dan
look closely at the last few problems in the picture that are not lettered they say- find angle ____

6. Originally Posted by peachgal
look closely at the last few problems in the picture that are not lettered they say- find angle ____
Uhhh... Oops!

Okay, for the top diagram, notice that angles JMN and MNP are supplementary. So
JMN + MNP = 180

Can you do the rest? (I got MNP = 28.)

For the bottom diagram, notice that both angles KGF and FGH are equal. (That's what the line crossing both the angle marks tells you.) So that tells us that
$\displaystyle 4x - 5 = 3x + 2$

$\displaystyle -3x + 4x - 5 = -3x + 3x + 2$

$\displaystyle x - 5 = 2$

$\displaystyle x - 5 + 5 = 2 + 5$

$\displaystyle x = 7$

So what is angle FGH? (I get FGH = 3x + 2 = 23 degrees.)

-Dan