Answer: The measure of the angle AED is 55°.
Step-by-step explanation:
Angles of Intersecting Chords Theorem, Two chords intersect in a circle internally ( or inside the circle), then the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
⇒ [tex]\angle AEC= \frac{180^{\circ}+70^{\circ}}{2}[/tex]
[tex]\implies \angle AEC =\frac{250}{2}=125^{\circ}[/tex]
Also, angles AEC and AED are linear pairs,
⇒ [tex]\angle AED+\angle AEC=180^{\circ}[/tex]
⇒ [tex]\implies \angle AED = 180^{\circ}-\angle AEC[/tex]
[tex]= 180^{/circ}-125^{\circ}=55^{\circ}[/tex]
Hence, the measure of the angle AED is 55°.
