Question

Exit ticket on angels,Arc and segments formed by intersecting chord,Secant,and tangents

Answer 1

The given information is:

- Arc FH measures 97°.

The measure of angle FGH is given by the formula:

$m\angle FGH=\frac{1}{2}(\hat{FIH}-\hat{FH})$

Now, the measure of the circumference is 360, so arc FIH measures:

$\begin{gathered} 360=FIH+FH \\ 360=FIH+97 \\ FIH=360-97 \\ FIH=263 \end{gathered}$

By replacing these values, we obtain:

$\begin{gathered} m\angle FGH=\frac{1}{2}(263-97) \\ m\angle FGH=\frac{1}{2}(166) \\ m\angle FGH=83\degree \end{gathered}$

The answer is angle FGH measures 83°.