Question

Please help soon!!
In the figure below, mZ1=2x° and mZ2=(x+96)
Find the angle measures.

Answer 1

We know that,

Sum of two angles in a linear pair = 180°

Therefore,

∠1 + ∠2 = 180°

=> (x - 18)° + 5x° = 180°

=> x° - 18° + 5x° = 180°

=> 6x° - 18° = 180°

=> 6x° = 180° + 18°

=> 6x° = 198°

=> x = 198°/ 6°

=> x = 33°

Now,

∠1 = (x - 18)°

= 33° - 18°

= 15°

∠2 = 5x°

= 5(33°)

= 165°

Therefore, the two angles are 15° and 165°

Answer 2

Here , we are going to use the property of linear pair . So , this property states that on any line , the sum of all angles formed by drawing other lines on the initial line is 180° or π radians .

__________________________

Coming back to the question , we are provided that ;

• 
  `{\sf \angle \: 1 = (x-18)^(\circ)}`

• 
  `{\sf \angle \: 2 = {5x}^(\circ)}`

Now by property of linear pair , we have ;

`{: \implies \quad \sf \angle \: 1 + \angle \: 2 = 180^(\circ)}`

Putting the values ;

`{: \implies \quad \sf x - 18^(\circ) + 5x = 180^(\circ)}`

`{: \implies \quad \sf 6x = 180^(\circ)+18^(\circ)}`

`{: \implies \quad \sf 6x=198^(\circ)}`

`{: \implies \quad \sf x = (198^(\circ))/(6)}`

`{: \implies \quad \sf x=33^(\circ)}`

Now , we can find measures of
`{\sf \angle \: 1}` &
`{\sf \angle \: 2}` , by putting the value of x

`{: \implies \quad \sf \angle \: 1 = (x-18)^(\circ)}`

`{: \implies \quad \sf \angle \: 1 = (33-18)^(\circ)}`

`{\boxed{\bf \therefore \quad \angle \: 1 = 15^(\circ)}}`

`{: \implies \quad \sf \angle \: 2 = {5x}^(\circ)}`

`{: \implies \quad \sf \angle \: 2 = {5* 33}^(\circ)}`

`{\boxed{\bf \therefore \quad \angle \: 2 = {165}^(\circ)}}`

We are Done :D