Question

determine the value of x in the following figure​

Answer 1

Step-by-step explanation:

GIVEN

BC = BD = CK

TO FIND = X

SOLUTION

ANGLE BCD = ANGLE BDC. (GIVEN)

ANGLE BDC + ANGLE BCD = 96°.

( SUM OF TWO ANGLES IS EQUAL TO THE OUTER OPPOSITE ANGLE)

X + X = 96°

2X = 96°

X = 96°/2

X = 48°

Answer 2

Answer:

96degrees

Step-by-step explanation:

We know, equal sides of a triangle subtend equal angles. So, ∠ABC = ∠ACB = ∠ADC = ∠CAD = x.

We also know that sum of all angles of a triangle is 180degrees.

So, ∠CAB = 180 -2x             . .(i)

On the straight line AD, we get,

x + ∠CAB + 96 = 180degrees    (adjacent angles)

x                        = 180 - 96 - ∠CAB

x                        = 84 - 180 + 2x      [using (i)]

x - 2x                 = -96

-x                       = -96

x                        = 96degrees

I hope you find the solution helpful :)