Question

current skill
1
2
3
5x + 6
5
7x + 42
7
8
find the measure of angle 2.
label optional

Explanation:

Step1: Find the value of \(x\)

Since \(5x + 6\) and \(7x+42\) are supplementary angles (they form a linear pair), we have the equation \(5x + 6+7x + 42=180\).
Combine like - terms: \(12x+48 = 180\).
Subtract 48 from both sides: \(12x=180 - 48=132\).
Divide both sides by 12: \(x=\frac{132}{12}=11\).

Step2: Find the measure of \(5x + 6\)

Substitute \(x = 11\) into \(5x + 6\): \(5\times11+6=55 + 6=61\).

Step3: Find the measure of angle 2

Since angle 2 and \(5x + 6\) are supplementary (they form a linear pair), \(\angle2=180-(5x + 6)\).
Substitute \(x = 11\) (we know \(5x + 6 = 61\)), so \(\angle2=180 - 61=119\).

Answer:

\(119\)