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.

Guest Oct 26, 2018

#3**+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

CPhill
Oct 26, 2018