Question

quadrilateral abcd is a rhombus measure of angle c is = (2 x + 4) ° and measure of angle adc is = (3 x + 6)° then find measure of angle cdequadrilateral abcd is a rhombus measure of angle c is = (2 x + 4) ° and measure of angle adc is = (3 x + 6)° then find measure of angle cde

Answer 1

Answer:

54

Step-by-step explanation:

i) question is repeated twice

ii) e is the mid point of abcd but it is not mentioned and directly asked that what is the measure of cde

with respect to the above points ,

in rhombus opposite angles are same , abc = adc and  dab = dcb

abc + adc + dab + dcb = 360 degree (angle sum property)

2 ( adc + dcb) = 360

adc + dcb = 360/2 = 180

(2 x + 4) °+ (3 x + 6)° = 180

5x + 10 = 180

5x = 180-10 = 170

x = 170/5 =  34

measure of angle c = (2 x + 4)  =  2(34) + 4 = 68 +4 = 72

measure of angle adc  = (3 x + 6)° = 3(34) + 6  = 102+6 = 108

we know that diagonals bisects the the angle of each side so ,  ade = cde

so, adc = ade + cde

adc =  2(cde)

cde = adc/2 = 108/2 = 54

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Answer 2

Answer:

72 degree

Step-by-step explanation:

given in answer key