Answer:
Angle g and h are complementary angles.
Angle g and h are acute angles.
Step-by-step explanation:
The given angles are
[tex]m\angle g=(2x-90)^{\circ}[/tex]
[tex]m\angle h=(180-2x)^{\circ}[/tex]
If sum of two angles is 180, then they called supplementary angles.
If sum of two angles is 90, then they called complimentary angles.
Add both angles.
[tex]m\angle g+m\angle h=(2x-90)^{\circ}+(180-2x)^{\circ}[/tex]
[tex]m\angle g+m\angle h=(2x-90+180-2x)^{\circ}[/tex]
[tex]m\angle g+m\angle h=90^{\circ}[/tex]
The sum of two angles is 90 degree, therefore angle g and h are complementary angles.
Both angles are greater than zero and their sum is 90, it means
[tex]0<\angle g<90[/tex] and [tex]0<\angle h<90[/tex]
Therefore, angle g and h are acute angles.
