Questions: Given the figure below, find the values of x and z.

Transcript text: Given the figure below, find the values of $x$ and $z$.

Solution

Solution Steps

Step 1: Find x

The angles measuring 93° and (7x + 31)° are vertical angles, and therefore congruent. Thus, we can set up the following equation:

7x + 31 = 93

Subtracting 31 from both sides gives:

7x = 62

Dividing both sides by 7 gives:

x = 62/7

Step 2: Find the value of the adjacent angle to 93°

The angle measuring z° and the angle measuring 93° are adjacent angles forming a straight line, so their sum is 180°. Let's call the angle adjacent to 93° 'y'.

y + 93 = 180

y = 180 - 93

y = 87°

Step 3: Find z

Since z° and y are vertical angles, they are congruent. Thus,

z = 87

Final Answer

x = 62/7 z = 87

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