We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Help!

0
277
3

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

### 3+0 Answers

#1
+1

135 degree

I can't explain due time being.

Oct 26, 2018
#2
+1

Yah I think 135 degrees is the answer

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