Question

ABcd is a rhombus and abe is an equilateral triangle, bcd =78. Calculate ade bde, bed

Answer 1

Answer:

<ADE = 21°

<BDE = 30°

<BED =39°

Step-by-step explanation:

It is given that, ABcd is a rhombus and ABE is an equilateral triangle,

< BCD=78.  therefore <BAD = 78 (opposite angles are equal)

From the figure attached with this answer,

All sides of rhombus and Sides of equilateral triangle are equal

Each angle in the triangle is 60

To find<ADE

<EAB = 60 (angle of equilateral triangle) and <BAD = 78°

<EAD = <EAB + <BAD = 60 + 78 =138°

Since AE = AD, <ADE = <AED

<ADE = 1/2(180 - 138) = 21°

To find <BDE

Triangle BCD  is an isosceles triangle,<BCD = 78°

and  <BDC = <DBC

<BDC = 1/2(180 - 78) = 51°

<ADC = 180 - 78 = 102°

<BDE = <ADC- <ADE - <BDC = 102 - 51 - 21= 30°

To find <BED

<BED = <AEB - <AED = 60 - 21 = 39°

Answer 2

Step-by-step explanation:

angle ade--->21°

angle bde--->30°

angle bed--->39°