Question

I need help pleaseeee!

Answer 1

115°

Explanation:

If two chords intersect inside a circle, the measure of one of the angles formed equals half the sum of its intercepted arc and that angle's vertical angle's intercepted arc.

For angle CHF, the two arcs are arc CDF and arc AB

so (100 + 60 + 30) + 40 = 230, times 1/2 = 115º

Answer 2

`m({\angle CHF})` = 115°

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})` =
`(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})` =
`(1)/(2)[40+190]`

= 115°

Therefore,
`m({\angle CHF})` = 115°