Question

circle F is intersected by line HI and IJ and the measurement of angle HIJ is 101 degrees. what is the measurement of arc HJ

Answer 1

To solve this problem, you need to use the Exterior Angle (Out) equation which for this problem would be
`(281-x)/(2)=101`. After correctly solving the problem with this equation, you will figure out that the answer is 79.

mHJ= 79°

Hope this helped :)

Answer 2

The the measurement of arc HJ is 79°.

Explanation:

Given information: Circle F intersected by HI and IJ and ∠HIJ=101°.

Let the measure of arc HJ be x°.

According the the angle of intersecting secant theorem,

Angle on the intersection of secants =
`(1)/(2)(\text{Major arc - Minor arc})`

`\angle HIJ=(1)/(2)(\text{Major arc(HJ) - Minor arc(HJ)})`

`101=(1)/(2)(281-x)`

Multiply both sides by 2.

`202=281-x`

`202-281=-x`

`-79=-x`

`79=x`

Therefore the measurement of arc HJ is 79°.