Question

find the measure of angle 4. 2x + 127 7x + 167

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Angle 4 and the angle with measure $2x + 127$ are vertical angles, and angle 5 and the angle with measure $7x+167$ are vertical angles. Also, angle 4 and angle 5 are supplementary (a linear - pair, so their sum is 180°). So, $(2x + 127)+(7x + 167)=180$.

Step2: Combine like terms

Combine the $x$ terms and the constant terms: $2x+7x+127 + 167=180$, which simplifies to $9x+294 = 180$.

Step3: Solve for $x$

Subtract 294 from both sides: $9x=180 - 294=- 114$. Then $x=\frac{-114}{9}=-\frac{38}{3}$.

Step4: Find the measure of angle 4

Since angle 4 has measure $2x + 127$, substitute $x =-\frac{38}{3}$ into the expression: $2\times(-\frac{38}{3})+127=\frac{-76}{3}+\frac{381}{3}=\frac{-76 + 381}{3}=\frac{305}{3}=101\frac{2}{3}$ degrees.

Answer:

$101\frac{2}{3}$ degrees