Question

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Answer 1

*Note that:-

• 9x+4= 3x+16 [Alternate interior angles]

Using this equation we will solve for x and then find each angle...

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`9x + 4 = 3x + 16 \\ 9x + 4 - 3x = 16 \\ 9x - 3x = 16 - 4 \\ 6x = 12 \\ x = 2`

Now,

`\large{|\underline{\mathsf{\red{1}\blue{ ^(s) }\orange{^(t) }\pink{ \: }\blue{a}\purple{n}\green{g}\red{l}\blue{e}\orange{ \: }\green{↯}\red{}\purple{}\pink{}}}}`

`\pmb{9x + 4} \\ \pmb{9 * 2 + 4} \\ \pmb{18 + 4} \\ \boxed{ \tt \: ∠1 = 22 \degree }`

`\large{|\underline{\mathsf{\red{2}\blue{ ^(n) }\orange{^(d) }\pink{ \: }\blue{a}\purple{n}\green{g}\red{l}\blue{e}\orange{ \: }\green{↯}\red{}\purple{}\pink{}}}}`

`\pmb{3x + 16} \\ \pmb{3 * 2 + 16} \\ \pmb{6 + 16} \\ \boxed{ \tt \: ∠2 = 22 \degree }`

Answer 2

We know that:

• 9x + 4 and 3x + 16 are equivalent because of alternate inner angles.

This means that:

• 
  `9x + 4 = 3x + 16`

Step-by step calculations:

Subtract 3x both sides.

• 
  `9x + 4 = 3x + 16`
• ⇒
  `9x - 3x + 4 = 3x - 3x + 16`
• ⇒
  `6x + 4 = 16`

Subtract 4 both sides.

• ⇒
  `6x + 4 = 16`
• ⇒
  `6x + 4 - 4 = 16 - 4`
• ⇒
  `6x = 12`

Divide 6 both sides.

• ⇒
  `(6x)/(6) = (12)/(6)`
• ⇒
  `x = 2`