Question

Circle R is shown where points
X,N,H and D
are on the circle. Some measurements are shown.
HN=79

and
XKD=104
What is the measure, in degrees, of XD
?

Answers

GPT-4o mini
To determine the measure of angle \( XD \) in circle \( R \) with the given points \( X, N, H, \) and \( D \), we need to analyze the provided information:

1. **Given**: \( HN = 79^\circ \) (This is the measure of arc \( HN \)).
2. **Given**: \( XKD = 104^\circ \) (This represents the angle at point \( K \) formed by lines \( XH \) and \( HD \)).

To find the measure of angle \( XD \):

- The angle \( XD \) subtends the same arc as angle \( HN \) since both angles are inscribed angles that intercept arc \( HD \).
- According to the Inscribed Angle Theorem, an inscribed angle is half the measure of the intercepted arc.

Thus, the measure of angle \( XD \) can be calculated as:

\[
XD = \frac{1}{2} \times HN
\]
\[
XD = \frac{1}{2} \times 79^\circ
\]
\[
XD = 39.5^\circ
\]

Therefore, the measure of angle \( XD \) is \( 39.5^\circ \).

Related Questions