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? 5. because vertical angles are congruent, (mangle deb=mangle aec). therefore, (mangle deb + mangle aec=square\times mangle deb). (mangle deb = 105^{circ}), (mangle aec = 105^{circ}), (moverparen{ac}=130^{circ}), (moverparen{bd}=80^{circ})

Explanation:

Step1: Recall vertical - angle property

Since $\angle DEB$ and $\angle AEC$ are vertical angles and $m\angle DEB=m\angle AEC = 105^{\circ}$, when we consider $m\angle DEB + m\angle AEC$, we substitute the values.

Step2: Calculate the sum

$m\angle DEB + m\angle AEC=105^{\circ}+ 105^{\circ}=2\times105^{\circ}$

Answer:

$2$