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 °