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 $m\angle aec = \boxed{105}^\circ$. 2. find the sum of the angle measures: $m\angle deb + m\angle aec = \boxed{210}^\circ$ 3. find the sum of the arc measures: $m\overarc{bd} + m\overarc{ac} = \boxed{\quad}^\circ$ given: $m\angle deb = 105^\circ$, $m\angle aec = 105^\circ$, $m\overarc{ac} = 130^\circ$, $m\overarc{bd} = 80^\circ$ (there is a diagram of a circle with chords $ad$ and $bc$ intersecting at point $e$.)

Explanation:

Step1: Identify given arc measures

We know that \( m\widehat{BD} = 80^\circ \) and \( m\widehat{AC} = 130^\circ \).

Step2: Sum the arc measures

To find the sum \( m\widehat{BD} + m\widehat{AC} \), we add the two given measures: \( 80^\circ + 130^\circ = 210^\circ \).

Answer:

210