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=\boxed{105})°. 2. find the sum of the angle measures: (mangle deb + mangle aec=\boxed{210})°. 3. find the sum of the arc measures; (mwidehat{bd}+mwidehat{ac}=) (mangle deb = 105^{circ}) (mangle aec = 105^{circ}) (mwidehat{ac}=130^{circ}) (mwidehat{bd}=80^{circ})

Explanation:

Step1: Identify given arc measures

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

Step2: Calculate sum of arc measures

$m\overparen{BD}+m\overparen{AC}=80 + 130$.

Answer:

$210$