Question

#6 find the missing angle.

Explanation:

Step1: Recall full circle angle sum

A full circle has $360^\circ$.

Step2: Sum known angles

Add given angles: $76^\circ + 119^\circ + 236^\circ = 431^\circ$

Step3: Calculate reflex angle error

Subtract full circle from sum: $431^\circ - 360^\circ = 71^\circ$

Step4: Find missing angle $x$

Subtract result from $180^\circ$ (linear pair): $x = 180^\circ - 71^\circ = 109^\circ$
*Note: The $236^\circ$ is a reflex angle, so the smaller angle between those two lines is $360^\circ - 236^\circ = 124^\circ$. Alternative check: $76^\circ + 119^\circ + 124^\circ + x = 360^\circ$, so $x = 360^\circ - 319^\circ = 41^\circ$ is incorrect. Correct approach: The $76^\circ$ is adjacent to $x$ and the $236^\circ$ reflex angle includes $119^\circ$ and the angle supplementary to $76^\circ$. The correct sum of non-reflex angles around the point is $360^\circ$, so $x = 360^\circ - (360^\circ - 236^\circ) - 76^\circ - 119^\circ = 236^\circ - 76^\circ - 119^\circ = 41^\circ$. Correction: The $236^\circ$ is the reflex angle, so the internal angle between those two lines is $360-236=124$. Then total angles: $76+119+124+x=360$. $76+119=195$, $195+124=319$, $360-319=41$.

Answer:

$41^\circ$