Question

in the given figure BC = CD angle find angle ACB​

Answer 1

Answer:

angle c is 74⁰

Step-by-step explanation:

The process is explained in the above pic

Hope it helps you !

Answer 2

Given:

A figure in which BC = CD, angle ADC = 116°, angle EAD = 138°.

To find:

angle ACB.

Solution:

As we know that the sum of all angles on one side of a straight line is equal to 180°.

Thus, from the figure we have,

angle ADC + angle BDC = 180°

116° + angle BDC = 180°

angle BDC = 180° - 116°

angle BDC = 64°

Also,

angles opposite to equal sides are equal, so,

as given,

BC = CD

Hence,

angle BDC = angle DBC = 64°

Now,

In a triangle DCB,

angle BDC + angle DBC + angle BCD = 180°

(some of the interior angles of a triangle is 180°)

64° + 64° + angle BCD = 180°

128° + angle BCD = 180°

angle BCD = 180° - 128° = 52°

angle BCD = 52°..(i)

Now,

angle EAD + angle DAC = 180°

138° + angle DAC = 180°

angle DAC = 180° - 138° = 42°

angle DAC = 42°

Also, in a triangle ADC,

angle DAC + angle ADC + angle ACD = 180°

42° + 116° + angle ACD = 180°

angle ACD = 180° - 158° = 22°

angle ACD = 22°.. (ii)

Now,

angle ACB = angle ACD + angle BCD

angle ACB = 22° + 52° (from i and ii)

angle ACB = 74°

Hence, angle ACB is 74°.