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

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 = $\frac{1}{2}(\text{Major arc - Minor arc})$

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

$101=\frac{1}{2}(281-x)$

Multiply both sides by 2.

$202=281-x$

$202-281=-x$

$-79=-x$

$79=x$

Therefore the measurement of arc HJ is 79°.

Answer 2

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

mHJ= 79°

Hope this helped :)