Question

find the value of x.
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x=

Explanation:

Step1: Use the angle - sum property of angles around a point

The sum of angles around a point is \(360^{\circ}\).
We have three angles of \((x - 2)^{\circ}\) and one angle of \(117^{\circ}\).
So, the equation is \(3(x - 2)+117=360\).

Step2: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), we get \(3x-6 + 117=360\).
Simplify the left - hand side: \(3x+111 = 360\).

Step3: Isolate the term with \(x\)

Subtract \(111\) from both sides of the equation: \(3x+111-111=360 - 111\).
We obtain \(3x=249\).

Step4: Solve for \(x\)

Divide both sides of the equation by \(3\): \(x=\frac{249}{3}\).

Answer:

\(x = 83\)