Question

parallelogram properties - angles
score: 0/5 penalty: 0.25 off
question
in parallelogram bcde if ( mangle bcd = 115^{circ} ) find ( mangle cde ).

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary. That is, the sum of adjacent angles is \(180^{\circ}\).
So, \(m\angle BCD + m\angle CDE=180^{\circ}\)

Step2: Substitute the given value

Given \(m\angle BCD = 115^{\circ}\), we substitute into the equation:
\(115^{\circ}+x^{\circ}=180^{\circ}\)

Step3: Solve for \(x\)

Subtract \(115^{\circ}\) from both sides of the equation:
\(x^{\circ}=180^{\circ}- 115^{\circ}\)
\(x^{\circ}=65^{\circ}\)

Answer:

\(65\)