Question

explore the properties of angles formed by two intersecting chords. make a conjecture. is the sum of the angle measures always equal to the sum of the arc measures? yes 5. because vertical angles are congruent, ( mangle deb = mangle aec ). therefore, ( mangle deb + mangle aec = square \times mangle deb ). options: 1/2, 2. ( mangle deb = 105^circ ), ( mangle aec = 105^circ ), ( moverarc{ac} = 130^circ ), ( moverarc{bd} = 80^circ )

Explanation:

Step1: Identify equal angles

Given \( m\angle DEB = m\angle AEC = 105^\circ \) (vertical angles are congruent).

Step2: Calculate the sum of angles

\( m\angle DEB + m\angle AEC = 105^\circ + 105^\circ = 210^\circ \).

Step3: Relate to \( m\angle DEB \)

We need to find a number \( x \) such that \( x \times m\angle DEB = 210^\circ \). Substitute \( m\angle DEB = 105^\circ \): \( x \times 105^\circ = 210^\circ \). Solving for \( x \), we get \( x=\frac{210^\circ}{105^\circ}=2 \).

Answer:

2