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A certain trapezoid has these properties: its diagonals are congruent and perpendicular to each other, and its longer base length is equal to the length of a diagonal. What is the sum of the degree measures of the two acute angles of this trapezoid.

 Oct 26, 2018
 #1
avatar+575 
+1

135 degree

I can't explain due time being.

 Oct 26, 2018
 #2
avatar+68 
+1

Yah I think 135 degrees is the answer

 Oct 26, 2018
 #3
avatar+98044 
+1

Thanks, Fiora and Sincerelyrose....

 

Here is the proof :

 

 

 

Since  BD   = AB...then angles ADB  and DAB  are equal

And angle AEB  = 90

And since the diagonals bisect each other...then AE  = BE

So...angles DBA  and CAB  are equal  = 45

 

Then...in triangle DAB....angle DBA  =  45

Andl angles DAB  and ADB  are equal....so

DAB  =  [180 - mDBA] / 2  =   [ 180 - 45 ] /  2 =   135 / 2  = 67.5

 

And...using the same sort of argument, we can show that angle  CBA  also  =  67.5

 

And.....these are the  two acute angles of the trapezoid....so their sum  = 135

 

 

cool cool cool 

 Oct 26, 2018
edited by CPhill  Oct 26, 2018
edited by CPhill  Oct 26, 2018

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