Question

There is a pair of vertical angles where < 1 = 106 degrees and <2 = 3x -75. What equation can you write to solve for x

Answer 1

There is a pair of vertical angles where ∠1=106° and ∠2=3x−75
so, 1 + 2 = 180
or, 106 + 3x - 75 = 180
3x = 180 -106 +75
3x = 149
x = 49.6
Hence, The solution is, the value is, x = 49.6.

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Answer 2

Vertical angles are always congruent, which means that they have the same measure. Therefore, we can set the measure of angle 1 equal to the measure of angle 2 and solve for x.

106 = 3x - 75

To solve for x, we can add 75 to both sides of the equation:

106 + 75 = 3x

Simplifying the left side:

181 = 3x

Finally, we can divide both sides by 3 to isolate x:

x = 60.33

Therefore, the value of x that makes the vertical angles congruent is approximately 60.33 degrees.