Question

I need help pleaseeee!

Answer 1

Answer:

$m({\angle CHF})$ = 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.

$m({\angle CHF})$ = $\frac{1}{2}[m(\widehat{AB}+m(\widehat{FC})]$ ---------(1)

$m(\widehat{AB})$ = 40°

$m(\widehat{FC})=m(\widehat{CD})+m(\widehat{DE})+m(\widehat{EF})$

$m(\widehat{FC})$ = 100° + 60° + 30°

           = 190°

By substituting these values in the expression (1)

$m({\angle CHF})$ = $\frac{1}{2}[40+190]$

                 = 115°

Therefore, $m({\angle CHF})$ = 115°