In parallelogram BCDE if m, angle, B, C, D, equals, 115, degreesm∠BCD=115

Question

∘
find m, angle, C, D, Em∠CDE.
B
C
D
E
115°
x°
Answer
Attempt 1 out of 2

x, equalsx=

Answer 1

In a parallelogram, opposite angles are equal and consecutive angles are supplementary (they add up to 180 degrees).

Given:

• \( m\angle BCD = 115^\circ \)

To find \( m\angle CDE \) (which is the same as \( m\angle B \)), we use the property that consecutive angles are supplementary:

\[ m\angle BCD + m\angle CDE = 180^\circ \]

Substituting the known angle:

\[ 115^\circ + m\angle CDE = 180^\circ \]

Now, we can solve for \( m\angle CDE \):

\[ m\angle CDE = 180^\circ - 115^\circ \] \[ m\angle CDE = 65^\circ \]

Thus, the measure of angle \( CDE \) is:

\[ \boxed{65^\circ} \]