Question

explore the properties of angles formed by two intersecting chords.
1.the intersecting chords form vertical angles. if $m\angle deb = 105^\circ$, then $m\angle aec = 105^\circ$.

1. find the sum of the angle measures: $m\angle deb + m\angle aec = 210^\circ$
2. find the sum of the arc measures: $m\overset{\frown}{bd} + m\overset{\frown}{ac} = \square^\circ$

$m\angle deb = 105^\circ$
$m\angle aec = 105^\circ$
$m\overset{\frown}{ac} = 130^\circ$
$m\overset{\frown}{bd} = 80^\circ$

Explanation:

Step1: Identify given arc measures

$m\widehat{AC}=130^\circ$, $m\widehat{BD}=80^\circ$

Step2: Calculate the sum of arcs

$m\widehat{BD} + m\widehat{AC} = 80^\circ + 130^\circ$

Answer:

210