Find the acute angle between the diagnols of a rectangle whose sides are 5 cm and 7 cm.

Question

The ans is 71.1 degree.

I don't know the method to solve it,

So please I request u to try to solve this sum I would really be thankful for it.

Answer 1

From Kenneth S.'s solution, m∠ACB = 35.54°

Draw a line line through the intersection of the diagonals parallel of CB.

Label the intersection of this line with AB as F.

∠AEF ≅ ∠ACB, by corresponding angles

m∠AEF = 35.54°

EF bisects ∠AEB

m∠AEF = m∠BEF 

m∠AEB = 2m∠AEF

m∠AEB = 71.08°

Answer 2

Draw the rectangle ABCD with side AB = 5, BC = 7.  Observe that tan ∠ACB = 5/7 so that angle is tan^-1(5/7) = 35.54^o.

 

Labelthe intersection of the DIAGONALS (check spelling) E; draw a line thru E and parallel to side

BC.  ⇐  bad typo corrected.

 

By alternate interior angles, there's an angle at E congruent to ∠ACB, measuring 35.54^o.

 

Angle DEC = two times that number, i.e. 71.08^o.  SEE WHY?