Question

ABCD is an inscribed quadrilateral whose diagonals intersect at F. Segment AB is parallel to segment DC, as shown below.



Prove that if angle DAC is 40° and angle ACD is 35°, then angle BDA is 70°. Write a two-column proof showing statements and reasons.

Answer 1

I really need help, last question!!!

Answer 2

Statement Reason
DAC is 40 Given
ACD is 35 Given

Answer 3

angle CBD is also 40 because they intercept the same arc...
yeah... i'm try to see how to make two triangles congurent..

Answer 4

angle CDA is 105 because the sum of angles in triangle CDA is 180

Answer 5

angle CFB and DFA are congruent becuase they're vertical angles.

Answer 6

triangle CFB and triangle DFA are similar by AAA
so <BCA = <ADB by corresponding similar triangles.

Answer 7

i am really stuck here....

Answer 8

i'm trying to see how <CDB is also 35 ... if we can do that then we're done...

Answer 9

any ideas?

Answer 10

hmm

Answer 11

idk

Answer 12

@precal do you have any ideas?

Answer 13

sorry @vepotter7 , i have to go.... i'll work on this later....

Answer 14

okay

Answer 15

@precal!!!

Answer 16

ok
angle CDB is 105
angle DAB is 35 according to the alt interior angles
angle BCD is 40 according to the alt interior angles
@dpaInc his angles are all correct
I hope that covers it, geometry is not my first love

Answer 17

thanks

Answer 18

anytime :)