Question

in the following figure find the value of x ​

Answer 1

Answer:

72°

Step-by-step explanation:

From the given figure we get to know that triangle DBC and ACD is an isosceles triangle.

so,

Angle DBC= Angle DCB and

Angle CAD= Angle CDA

so, angle C = 27°

Now,

angle CDB = 126° ( Angle Sum Property)

Now, Angle CDB and CDA are in linear pair.

this means

Angle CDB+Angle CDA = 180°

this means

126°+ CDA= 180°

so,

Angle CDA= 54°

Now, CDA= CAD

so CAD=54°

Now, x= 72° (Angle Sum Property)

Answer 2

Answer:

BD=DC

ANG. DBC = ANG. DCB (ANG. OPP. TO EQUAL SIDES ARE EQUAL)

DCB = 27°

ACB= 27+X

DBC + BDC + BCD = 180 (ANG. SUM PROP.)

BDC + 27 + 27 =180

BDC = 180- 54

BDC = 126°

BDC + ADC = 180° (LINEAR PAIR)

126 + ADC = 180

ADC = 54°

DC = AC

ANG. ADC = ANG. DAC (ANG. OPP. TO EQUAL SIDES ARE EQUAL)

DAC = 54°

ABC + BAC + BCA = 180°(ANG. SUM PROP.)

27 + 27+X +54 = 180

54+54+X = 180

108 + X = 180

X = 180- 108

X = 72°

Hence, X = 72°

So I think this is the right answer

thanks