Question

explore the properties of angles formed by two intersecting chords. 1. the intersecting chords form vertical angles. if m∠deb = 105°, then m∠aec = 105 °. 2. find the sum of the angle measures: m∠deb + m∠aec = 210 °. 3. find the sum of the arc measures: mbd + mac = °. m∠deb = 105° m∠aec = 105° mac = 130° mbd = 80°

Explanation:

Step1: Identify given arc measures

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

Step2: Calculate the sum of arc measures

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

Answer:

\( 210 \)