Question

explore the properties of angles formed by two intersecting chords.
1.the intersecting chords form vertical angles. if (mangle deb = 105^{circ}), then (mangle aec=)

1. find the sum of the angle measures: (mangle deb + mangle aec=)
2. find the sum of the arc measures: (moverparen{bd}+moverparen{ac}=)

(mangle deb = 105^{circ})(mangle aec = 105^{circ})(moverparen{ac}=130^{circ})(moverparen{bd}=80^{circ})

Explanation:

Step1: Identify given arc - measures

Given $m\overparen{BD}=80^{\circ}$ and $m\overparen{AC}=130^{\circ}$.

Step2: Calculate sum of arc - measures

We need to find $m\overparen{BD}+m\overparen{AC}$.
$m\overparen{BD}+m\overparen{AC}=80 + 130$.

Answer:

$210$