Question

current skill
show answer
7x + 119
-7x + 77
find the measure of angle 5.

Explanation:

Step1: Find the value of \(x\)

Since \(7x + 119\) and \(-7x+77\) are supplementary angles (they form a linear pair), we have the equation \(7x + 119+(-7x + 77)=180\).
Simplify the left - hand side:

$$
LATEXBLOCK0
$$

Wait, this is wrong. Actually, \(7x + 119\) and \(-7x + 77\) are same - side interior angles. If the lines are parallel (assumed from the angle - pair setup), then \(7x+119=-7x + 77\) (because they are congruent as alternate interior angles).

$$
LATEXBLOCK1
$$

Step2: Find the measure of angle \(5\)

Substitute \(x =-3\) into the expression for the angle adjacent to \(7x + 119\) (angle \(5\) and \(7x + 119\) are supplementary).
First, find \(7x+119\) when \(x=-3\): \(7\times(-3)+119=-21 + 119 = 98\)
Since angle \(5\) and \(7x + 119\) are supplementary (they form a linear pair), let \(m\angle5=y\). Then \(y+(7x + 119)=180\)
Substitute \(x=-3\) into the equation: \(y+98 = 180\)

$$y=180 - 98=82$$

Answer:

\(82^{\circ}\)