Question

In the above figure, m(arc DXE) = 105°, m(Arc AYC) = 47°, then find the measure of ∠DBE.

Answer 1

Chord AD and CE intersect externally at point B.

When two secants (or chords extended) intersect outside a circle, the measure of the angle formed is half the difference of the measures of the intercepted arcs.

∴ m∠DBE = `1/2["m"("arc"  "DXE") - "m"("arc"  "AYC")]` 

∴ m∠DBE = `1/2 [105^circ - 47^circ]`

∴ m∠DBE = `1/2[58^circ]`

∴ m(∠DBE) = 29°