Question

Given the figure below, find the values of x and z.
108
(12x+24)

Answer 1

We calculate "x":

We know that two vertical angles are equal.

`108° \: = \: (12x \: + \: 24)°`

`- 12x \: = \: 24 \: - \: 108`

`- 12x \: = \: -84`

`\boxed{ \bold{x \: = \: 7°}}`

We calculate "x":

We know that a complete angle measures 360°.

`108° \: + \: 108° \: + \: z \: + \: z \: = \: 360°`

`216 \: + \: 2z \: = \: 360`

`2z \: = \: 360 \: - \: 216`

`2z \: = \: 144`

`\boxed{ \bold{z \: = \: 72°}}`

Answer:

• x = 7
• z = 72 °