Question

Can you help me solve this?

Answer 1

`\underline{ \text{See \: below}}`

Explanation:

`\text{Given} :`

• 
  `\sf{m \: \angle \: F\: = \: (4x - 5 ) \degree }`
• 
  `\sf{m \: \angle \: F\: = (3x + 1) \degree}`
• 
  `\sf{ \: m \angle \: H \: = \: x \degree}`

`\underline{ \text{First, \: finding \: the \: value \: of \: x}}`:

`\sf{m \angle \: F\: + \: m \angle \: G \: + \: m \angle \: H \: = 180 \: \degree}`

`\text{➳ \: 4x - 5 + 3x + 1 + x = 180 \degree }`

`\text{➳ \: 8x - 4 = 180 \degree}`

`\text{➳8x = 180 \degree + 4}`

`\text{➳8x = 184 \degree}`

`\text{ ➳\: 8x \: / \: 8 \: = \: 184 \degree \: / \: 8}`

`\text{➳x = \: 23 \degree}`

`\boxed{ \sf{ m \angle \: H\: = \: 23 \degree}}`

`\underline{ \sf{Replacing \: the \: value \: of \: x \: in \: order \: to \: find \: the \: value \: of \: m \angle \: F}} :`

`\sf{➳m \angle \: F\: = \: \: (4x - 5)°}`

`\sf{➳m \angle \: F \: = (4 * 23 - 5)°}`

`\sf{➳ m \angle \: F\: = (92 - 5)°}`

`\boxed{ \sf{m \angle \: F \: = 87°}}`

`\underline{ \sf{Replacing \: the \: value \: of \: x \: in \: order \: to \: find \: the \: value \: m \angle \: G}} :`

`\sf{➳ \: m \angle \: G\: = \: (3x + 1)°}`

`\sf{➳ \: m \angle \: G \: = ( 3 \: * \: 23 + 1)°}`

`\sf{➳ \: m \angle \: G\: = (69 + 1)°}`

`\boxed{ \sf{m \angle \: G\: = 70°}}`

`\text{Hope \: i \: helped!}`

`\text{Best \: regards!}`

~
`\text{TheAnimeGirl}`