Question

current skill! find the measure of angle 7. -2x + 33 -4x - 5 2 1 3 6 8 7

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Angle $(-2x + 33)$ and angle $(-4x - 5)$ are vertical angles, so $-2x+33=-4x - 5$.

Step2: Solve the equation for x

Add $4x$ to both sides: $-2x + 4x+33=-4x+4x - 5$, which simplifies to $2x+33=-5$. Then subtract 33 from both sides: $2x+33 - 33=-5 - 33$, so $2x=-38$. Divide both sides by 2: $x=-19$.

Step3: Find the measure of angle 7

Substitute $x = - 19$ into the expression for angle 7. Angle 7 is adjacent - supplementary to the angle $(-4x - 5)$. First, find the measure of $-4x - 5$ when $x=-19$. $-4(-19)-5=76 - 5=71$. Since angle 7 and $(-4x - 5)$ are supplementary (sum to 180°), angle 7 is $180 - 71 = 109$.

Answer:

109