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

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

mHJ= 79°

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erinna erinna · Answer 2 · 2019-07-22T11:47:16+02:00

Answer:

The the measurement of arc HJ is 79°.

Step-by-step 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 = [tex]\frac{1}{2}(\text{Major arc - Minor arc})[/tex]

[tex]\angle HIJ=\frac{1}{2}(\text{Major arc(HJ) - Minor arc(HJ)})[/tex]

[tex]101=\frac{1}{2}(281-x)[/tex]

Multiply both sides by 2.

[tex]202=281-x[/tex]

[tex]202-281=-x[/tex]

[tex]-79=-x[/tex]

[tex]79=x[/tex]

Therefore the measurement of arc HJ is 79°.