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

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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

#4
+109524
+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
+109524
+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.

BUT

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

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.

Dec 12, 2015
edited by Melody  Dec 12, 2015
edited by Melody  Dec 12, 2015
#2
+111329
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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

Dec 12, 2015
edited by CPhill  Dec 12, 2015
#3
+111329
+5

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

Dec 12, 2015
#4
+109524
+15

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
+111329
+10

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

Dec 12, 2015
#6
+109524
+5

I just used GeoGebra :)

Dec 13, 2015