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

2 Answers

7 votes

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

User Mfreiholz
by
7.7k points
7 votes

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
$\angle BDC$.

User Laxmana
by
9.0k points

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