Question

current skill
find the measure of angle 6.
label optional

Explanation:

Step1: Identify vertical angles

Vertical angles are equal, so $8x + 78 = 9x + 153$.

Step2: Solve for x

Subtract $8x$ from both sides: $78 = x + 153$. Subtract 153: $x = -75$.

Step3: Find angle 4

Angle 4 = $8(-75) + 78 = -600 + 78 = -522$ (invalid, assume typo: should be supplementary angles). Correct: $8x + 78 + 9x + 153 = 180$. Combine terms: $17x + 231 = 180$. $17x = -51$. $x = -3$.

Step4: Calculate angle 6 (equal to angle 4)

Angle 4 = $8(-3) + 78 = -24 + 78 = 54$. So angle 6 = 54.

Answer:

54