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

Given in the figure below, find the values of X and Z.-example-1
User Mukul Kant
by
8.9k points

1 Answer

2 votes

Answer:


\boxed{x=9}\\\boxed{z=76}

Explanation:

Hello There!

Geometry

The angles shown represented by the expressions (11x + 5) and (5x+59) are vertical angles

Vertical angles are congruent so we can use this equation to solve for x

Basic Algebra

11x + 5 = 5x + 59

step 1 subtract 5x from each side

5x - 5x cancels out

11x - 5x = 6x

now we have 6x + 5 = 59

step 2 subtract each side by 5

5 - 5 cancels out

59 - 5 = 54

now we have 54 = 6x

step 3 divide each side by 6

6x/6=x

54/6=9

we're left with x = 9

now we want to plug in 9 into x for one of the expression

11(9) + 5

11 * 9 = 99

99 + 5 = 104

so we can conclude that the measure of the angle labeled ( 11x + 5 ) is 104 degrees

Now we need to find z

Geometry

The angle with a measure of 104 and angle Z are supplementary angles meaning that the sum of the two is 180

So to find z we subtract the known angle (104) from 180

180 - 104 = 76

so we can conclude that z = 76

User Tennile
by
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