Question

#4 find the unknown value
119
61
30.5
122

Explanation:

Step1: Identify central angle rule

A full circle is $360^\circ$. The unknown angle and $61^\circ$ form a pair of angles that are vertical to the other two angles, but more directly, the unknown angle is supplementary to $61^\circ$? No, wait: the unknown angle and $61^\circ$ are adjacent to form a straight line? No, the circle is split into 4 parts, with two pairs of vertical angles. Wait, no: the sum of angles around a point is $360^\circ$. The unknown angle is vertical to the angle opposite? No, no: the angle supplementary to $61^\circ$ would be $180-61=119$? No, wait, no: the unknown angle is the one that, with $61^\circ$, adds up to $180^\circ$? No, wait, the circle: the two angles, $61^\circ$ and the unknown, are adjacent, and the other two angles are equal to these two. Wait, no: the sum of all angles is $360^\circ$. If the unknown angle is $x$, then $2\times61^\circ + 2x = 360^\circ$.

Step2: Solve for x

First calculate $2\times61^\circ = 122^\circ$. Then $360^\circ - 122^\circ = 238^\circ$. Then $x = \frac{238^\circ}{2} = 119^\circ$.
Alternatively, since adjacent angles around a point on a straight line sum to $180^\circ$, so $x = 180^\circ - 61^\circ = 119^\circ$.

Answer:

119