Question

ABCD is a rhombus and ABE is an equilateral triangle surmounted on the side AB. Angle BCD = 78°. Calculate Angles ADE, BDE and BED. (Fig. is given)​

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

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