Answer:
[tex] \underline{ \text{See \: below}}[/tex]
Step-by-step explanation:
[tex] \text{Given} : [/tex]
- [tex] \sf{m \: \angle \: F\: = \: (4x - 5 ) \degree }[/tex]
- [tex] \sf{m \: \angle \: F\: = (3x + 1) \degree}[/tex]
- [tex] \sf{ \: m \angle \: H \: = \: x \degree}[/tex]
[tex] \underline{ \text{First, \: finding \: the \: value \: of \: x}}[/tex]:
[tex] \sf{m \angle \: F\: + \: m \angle \: G \: + \: m \angle \: H \: = 180 \: \degree}[/tex]
[tex] \text{➳ \: 4x - 5 + 3x + 1 + x = 180 \degree }[/tex]
[tex] \text{➳ \: 8x - 4 = 180 \degree}[/tex]
[tex] \text{➳8x = 180 \degree + 4}[/tex]
[tex] \text{➳8x = 184 \degree}[/tex]
[tex] \text{ ➳\: 8x \: / \: 8 \: = \: 184 \degree \: / \: 8}[/tex]
[tex] \text{➳x = \: 23 \degree}[/tex]
[tex] \boxed{ \sf{ m \angle \: H\: = \: 23 \degree}}[/tex]
[tex] \underline{ \sf{Replacing \: the \: value \: of \: x \: in \: order \: to \: find \: the \: value \: of \: m \angle \: F}} : [/tex]
[tex] \sf{➳m \angle \: F\: = \: \: (4x - 5)°}[/tex]
[tex] \sf{➳m \angle \: F \: = (4 \times 23 - 5)°}[/tex]
[tex] \sf{➳ m \angle \: F\: = (92 - 5)°}[/tex]
[tex] \boxed{ \sf{m \angle \: F \: = 87°}}[/tex]
[tex] \underline{ \sf{Replacing \: the \: value \: of \: x \: in \: order \: to \: find \: the \: value \: m \angle \: G}} : [/tex]
[tex] \sf{➳ \: m \angle \: G\: = \: (3x + 1)°}[/tex]
[tex] \sf{➳ \: m \angle \: G \: = ( 3 \: \times \: 23 + 1)°}[/tex]
[tex] \sf{➳ \: m \angle \: G\: = (69 + 1)°}[/tex]
[tex] \boxed{ \sf{m \angle \: G\: = 70°}}[/tex]
[tex] \text{Hope \: i \: helped!}[/tex]
[tex] \text{Best \: regards!}[/tex]
~[tex] \text{TheAnimeGirl}[/tex]
