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

Answer 1

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

Given that \( m\angle BCD = 115^\circ \), we can find the measure of angle \( CDE \) as follows:

1. Since opposite angles are equal: \[ m\angle B = m\angle D = 115^\circ \]

2. Now, to find the measure of angle \( CDE \): \[ m\angle CDE = 180^\circ - m\angle BCD \] \[ m\angle CDE = 180^\circ - 115^\circ = 65^\circ \]

Thus, \( m\angle CDE = 65^\circ \).