Question

Circle
D
D is shown where points
N
,

H
,
N, H, and
X
X are on the the circle and
m
N
H
⏠
=
104
°
.
m
NH
=104°. Triangle
N
X
H
NXH is an isosceles triangle where
X
N
‾
≅
H
N
‾
.
XN
≅
HN
.

Answer 1

is this right?

Answer 2

Given the information about circle \(D\), the points \(N\), \(H\), and \(X\) are located on the circle with the angle \(m \angle NHX = 104^\circ\). Since triangle \(NXH\) is isosceles with \(XN \cong HN\), we can use the properties of isosceles triangles and angles to determine the measures of the other angles in triangle \(NXH\).

In an isosceles triangle, the angles opposite the equal sides are equal. Let’s denote the angles in triangle \(NXH\) as follows:

- Let \(m \angle XNH = m\angle HXN = x\).

Since the sum of the angles in any triangle equals \(180^\circ\), we can write the equation:

\[
x + x + 104^\circ = 180^\circ
\]

Combining like terms:

\[
2x + 104^\circ = 180^\circ
\]

Now, isolate \(x\):

\[
2x = 180^\circ - 104^\circ
\]
\[
2x = 76^\circ
\]
\[
x = \frac{76^\circ}{2}
\]
\[
x = 38^\circ
\]

Thus, we find that:

- \(m \angle XNH = 38^\circ\)
- \(m \angle HXN = 38^\circ\)
- \(m \angle NHX = 104^\circ\)

In summary, the measures of the angles in triangle \(NXH\) are:

- \(m \angle XNH = 38^\circ\)
- \(m \angle HXN = 38^\circ\)
- \(m \angle NHX = 104^\circ\)