Answer:
[tex]m({\angle CHF})[/tex] = 115°
Step-by-step explanation:
Intersecting chord theorem,
"When two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle."
By this theorem.
[tex]m({\angle CHF})[/tex] = [tex]\frac{1}{2}[m(\widehat{AB}+m(\widehat{FC})][/tex] ---------(1)
[tex]m(\widehat{AB})[/tex] = 40°
[tex]m(\widehat{FC})=m(\widehat{CD})+m(\widehat{DE})+m(\widehat{EF})[/tex]
[tex]m(\widehat{FC})[/tex] = 100° + 60° + 30°
= 190°
By substituting these values in the expression (1)
[tex]m({\angle CHF})[/tex] = [tex]\frac{1}{2}[40+190][/tex]
= 115°
Therefore, [tex]m({\angle CHF})[/tex] = 115°
