Question

Given in the figure below, find the values of X and Z.

Answer 1

x = 6

z = 79

Explanation:

We know that angles on a straight line add up to 180.

With this in mind:

• (6x+43)° + (8x+53)° = 180
• hence 14x+96=180
• 14x=84
• x=6

For z:

• since x = 6
• (8x+53)° + z° = 180
• 101 + z = 180
• z = 79

Another approach using the property where opposite angles are equal:

• (6x+43) = z
• 79 = z

Answer 2

x = 6 , z = 79

Explanation:

(8x + 53) and (6x + 43) are adjacent angles and sum to 180° , that is

8x + 53 + 6x + 43 = 180 , that is

14x + 96 = 180 ( subtract 96 from both sides )

14x = 84 (divide both sides by 14 )

x = 6

Then

6x + 43 = 6(6) + 43 = 36 + 43 = 79

z and 79 are vertical angles and congruent , then

z = 79