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In trapezoid ABCD, BC || AD, angle ABD =105°, angle A=43°, and angle C=141°. Find angle CBD, in degrees.

 Dec 12, 2015

Best Answer 

 #4
avatar+99356 
+15

Hi Chris,

 

Scaled pic

Drawing these pics to scale is always a time consuming but pleasant challenge :)

 Dec 12, 2015
edited by Melody  Dec 12, 2015
 #1
avatar+99356 
+15

Hi Mellie,

In trapezoid ABCD, BC || AD, angle ABD =105°, angle A=43°, and angle C=141°. Find angle CBD, in degrees.

 

 

ok, the first thing I did is tried to work out what the trapezium looked like. 

THEN the answer became obvious.

BUT

it also became ovvious that I did not need to know what the trapezium looked like in ordet to answer this question.

 

Draw ANY trapezium where BC||AD

Label <ABD as 105 degrees.   (It doesn't need to LOOK anythink like 105 degrees, mine looks like an acute angle)

Label <A as 43 degrees 

Label < C as 141 degrees

 

Now you can see that <CBD is an alternate angle on parallel lines to <BDA. So they are congruent.

< BDA+105+43=180     Angle sum of triangle ABD

<BDA = 32 degrees

 

Therefore <CBD = 32 degrees

 

Here is a diagram most definitely not to scale.   frown

 Dec 12, 2015
edited by Melody  Dec 12, 2015
edited by Melody  Dec 12, 2015
 #2
avatar+98196 
+10

 ABD = 105° and ABD will form a triangle.....then angle ADB will  =   180 - 43  -105 = 32°

 

And, since AD is parallel to BC,  angle CBD will have the same measure as angle ABD  = 32°    because they are alternating interior angles between  these parallels

 

 

 

 

cool cool cool

 Dec 12, 2015
edited by CPhill  Dec 12, 2015
 #3
avatar+98196 
+5

Nice pic, Melody........this one would be difficult to "scale" properly.....

 

 

 

cool cool cool

 Dec 12, 2015
 #4
avatar+99356 
+15
Best Answer

Hi Chris,

 

Scaled pic

Drawing these pics to scale is always a time consuming but pleasant challenge :)

Melody Dec 12, 2015
edited by Melody  Dec 12, 2015
 #5
avatar+98196 
+10

What program did you use for that.......????......I like it.....!!!

 

 

 

 

cool cool cool

 Dec 12, 2015
 #6
avatar+99356 
+5

I just used GeoGebra :)

 Dec 13, 2015

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