Question

find the measure of angle 4. 9x - 25 -4x + 157

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle 4 and the angle with measure $- 4x + 157$ are vertical angles, and the angle with measure $9x-25$ and the angle adjacent to $-4x + 157$ (let's call it $\angle A$) are vertical angles. Also, $\angle A$ and $-4x + 157$ are supplementary (linear - pair), so $(9x - 25)+(-4x + 157)=180$.

Step2: Solve the equation for x

Combine like terms: $9x-4x-25 + 157=180$.
$5x+132 = 180$.
Subtract 132 from both sides: $5x=180 - 132=48$.
Divide both sides by 5: $x=\frac{48}{5}=9.6$.

Step3: Find the measure of angle 4

Since angle 4 has the same measure as $-4x + 157$, substitute $x = 9.6$ into $-4x + 157$.
$-4\times9.6+157=-38.4 + 157 = 118.6$.

Answer:

$118.6$