Question

current skill
find the measure of angle 7.
7
8
5
7x + 187
3
4
2
-5x + 31

Explanation:

Step1: Identify angle - pair relationship

Angles \(7x + 187\) and \(- 5x+31\) are vertical angles. Vertical angles are equal.
So, \(7x + 187=-5x + 31\).

Step2: Solve the equation for \(x\)

Add \(5x\) to both sides: \(7x+5x + 187=-5x+5x + 31\), which simplifies to \(12x+187 = 31\).
Then subtract 187 from both sides: \(12x+187 - 187=31 - 187\), giving \(12x=-156\).
Divide both sides by 12: \(x=\frac{-156}{12}=-13\).

Step3: Find the measure of an angle related to angle 7

Substitute \(x = - 13\) into the expression for the angle adjacent to angle 7 (say the angle \(7x + 187\)).
\(7(-13)+187=-91 + 187 = 96\).
Angle 7 and the angle \(7x + 187\) are supplementary (linear - pair, sum to \(180^{\circ}\)).
Let the measure of angle 7 be \(y\). Then \(y+96^{\circ}=180^{\circ}\).

Step4: Calculate the measure of angle 7

Subtract 96 from both sides: \(y=180 - 96=84^{\circ}\).

Answer:

\(84^{\circ}\)