Question

What is mZIFU? J G X+16° X+350 55° 2x-700 H T

Answer 1

Ìn a circle the sum of all the central angles sum 360º.

Then, for the given circle:

$m\angle IFJ+m\angle JFG+m\angle GFH+m\angle HFI=360º$$(x+35º)+(x+16º)+(55º)+(2x-70º)=360º$

You use the equation above to find the value of x:

$\begin{gathered} x+35+x+16+55+2x-70=360 \\ 4x+36=360 \\ 4x+36-36=360-36 \\ 4x=324 \\ \frac{4}{4}x=\frac{324}{4} \\ \\ x=81 \end{gathered}$

With the value of x you find the measure of angle IFJ:

$m\angle IFJ=x+35=81+35=116º$Then, the measure of angle IFJ is 116º