Question

The diagonals of rhombus ABCD intersect at E. Given that m∠CAD=20° and CE=4, find the m∠CDA.

Answer 1

< CDA = 140 degrees

Explanation:

For a rhombus, the sum of the interior angles is 360 degrees and also the opposite angles are equal i.e <ABC = <CDA and <BAD = <BCD

Given

<CAD = 20 degrees

<BCE = 20 degrees (based on geometry)

<BAD = <CAD + <BCE

<BAD = 20 + 20

<BAD = 40 degrees

Since <BAD = <BCD, then <BCD = 40 degrees

Get <CDA

<CDA + <ABC + <BAD + <BCD = 360

<CDA + <CDA + <BAD + <BCD = 360

2 < CDA + 40 + 40 = 360

2< CDA + 80 = 360

2< CDA = 360-80

2< CDA = 280

< CDA = 280/2

< CDA = 140 degrees