Question

current skill show answer (2) request find the measure of angle 6.

Explanation:

Step1: Set up the equation

Since \(3x + 87\) and \(-3x + 141\) are supplementary angles (they form a linear pair), we have the equation \((3x + 87)+(-3x + 141)=180\). But we can also use the property that \(3x + 87=-3x + 141\) (vertical - angle relationship).

$$3x+87=-3x + 141$$

Step2: Solve for \(x\)

Add \(3x\) to both sides:

$$3x+3x+87=-3x + 3x+141$$

$$6x+87 = 141$$

Subtract \(87\) from both sides:

$$6x+87-87=141 - 87$$

$$6x=54$$

Divide both sides by \(6\):

$$x = 9$$

Step3: Find the measure of \(\angle6\)

Substitute \(x = 9\) into the expression for \(\angle6\). First, find the measure of the angle adjacent to \(\angle6\) (using \(3x + 87\)). When \(x = 9\), \(3x+87=3\times9 + 87=27+87 = 114\). Since \(\angle6\) and \(3x + 87\) are supplementary (linear - pair), \(\angle6=180-(3x + 87)\).

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Answer:

\(66\)