Question

In the following figure , find the value of x​

Answer 1

Answer:

Given angle DBC = 27°

To find angle x

Here angle DBC = angle DCB ( angles opposite to equal sides are equal)

therefore , angle DCB = 27°

angle DCB+ angle DCB +angle BDC = 180°

(angle sum property of triangle)

27° + 27° + angle BDC = 180°

angle BDC = 180° - 54°

angle BDC = 136°

angle BDC + angle ADC = 180°

(Forms a straight line)

136°+angle ADC = 180°

angle ADC = 180° - 136°

angle ADC = 54°

angle ADC = angle CAD (angles opposite to equal sides are equal)

therefore, angle CAD = 54°

angle ADC + angle CAD + angle ACD = 180°

(angle sum property of triangle)

54°+54°+angle ACD = 180°

angle ACD = 180° - 108°

angle ACD = 72°

therefore, angle ACD ( x ) = 72°