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katen-ka-za [31]
3 years ago
7

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

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
5 0

Answer:

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

Step-by-step explanation:

Hello There!

<u>Geometry</u>

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

<u>Basic Algebra</u>

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

<u>Geometry</u>

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

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