Question

If abcd is a rectangle and m cbd 47 what is the value of x

Answer 1

The value of x is
`\(86^\circ\)`. So correct option is D.

In a rectangle, opposite angles are equal, so if ∠CBD is given as 47 degrees, then ∠BCD is also 47 degrees.

Since CBD is a right angle (as it's part of a rectangle), the sum of angles in triangle CBD is 180 degrees. Therefore:

`\[ \text{∠CDB} + \text{∠CBD} + \text{∠BCD} = 180^\circ \]`

Let x be the measure of ∠CDB. Plug in the known values:

`\[ x + 47^\circ + 47^\circ = 180^\circ \]`

Combine like terms:

`\[ x + 94^\circ = 180^\circ \]`

Now, isolate x:

`\[ x = 180^\circ - 94^\circ \]`

`\[ x = 86^\circ \]`

So, the value of x is
`\(86^\circ\)`. So correct option is D.

Complete Question: If ABCD is a rectangle and m∠ CBD=47° , what is the value of x?

A. 47

B. 133

C. 94

D. 86

E. 43

F. Cannot be determined

Answer 2

The value of x is 86.

To find the value of x in the given rectangle
`$ABCD$`, we need to use the fact that the opposite angles in a rectangle are congruent.

Since
`$\angle CBD = 47^\circ$`, we know that
`$\angle CDB$` is also
`$47^\circ$`. Similarly, since
`$ABCD$` is a rectangle, we have
`$\angle ABC = \angle ADC = 90^\circ$`.

Now, let's focus on triangle
`$BCD$`. The sum of the angles in a triangle is always
`$180^\circ$`. So, we can write an equation based on the angles in triangle
`$BCD$`:

`$\angle CDB + \angle CBD + \angle BDC = 180^\circ$`

Substituting the given values:

`$47^\circ + 47^\circ + \angle BDC = 180^\circ$`

Simplifying:

`$94^\circ + \angle BDC = 180^\circ$`

Subtracting
`$94^\circ$` from both sides:

`$\angle BDC = 180^\circ - 94^\circ$`

`$\angle BDC = 86^\circ$`

Since
`$\angle BDC$` is an angle in a triangle, it must be less than
`$180^\circ$`. Therefore,
`$86^\circ$` is a valid value for
`$\angle BDC$`.