Question

In circle O. chord EZ intersects chord I at K such that mHE-88°.mEl-112°, and mIZ=114⁹

of the following represents the measure of ZHKZ?
(1) 23⁰
(3) 79⁰
(2) 60°
(4) 101°

Answer 1

1) 23 degrees

Explanation:

What is a chord? A chord is a line segment that intersects another chord in a circle at 2 points. The angle formed by the 2 chords is half of the arc measure of the 2 points.

Given this definition, we can see that <HKZ has to be half of the arc HZ.

To find HZ, add up the other arc measures and subtract from 360 degrees:

360-(88+112+114)

=46

This means that HZ is 46 degrees.

Like I said before, <HKZ has to be half of HZ, which is 46, so:

46/2

=23

This makes <HKZ 23 degrees.

Hope this helps! :)