Question

explore the properties of angles formed by two intersecting chords.
therefore,
m∠deb + m∠aec =
2 × m∠deb.

1. by

2(m∠deb)=mbd + mac, or
m∠deb = 1/2 (mbd + mac).
m∠deb = 105°
m∠aec = 105°
mac = 130°
mbd = 80°

Explanation:

Step1: Recall the theorem

The measure of an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs.

Step2: Identify given values

We are given \(m\angle DEB = 105^{\circ}\), \(m\widehat{AC}=130^{\circ}\), and \(m\widehat{BD} = 80^{\circ}\). And the formula \(m\angle DEB=\frac{1}{2}(m\widehat{BD}+m\widehat{AC})\) holds true as \(\frac{1}{2}(80 + 130)=\frac{1}{2}(210)=105\). The missing concept is the theorem about angles formed by intersecting chords.

Answer:

The theorem about angles formed by intersecting chords in a circle.