Question

what is the value of c?

Explanation:

Step1: Recall the sum of angles around a point

The sum of angles around a point is \(360^{\circ}\). But here, we can also note that the angles \(c\), \(68^{\circ}\), \(78^{\circ}\) and the vertical - opposite angle relationships. However, a simpler way is to use the fact that the sum of angles on a straight - line is \(180^{\circ}\). Wait, no, actually, if we consider the full - circle sum. But another approach: since the non - \(c\) angles: two pairs of vertical angles. Wait, no. Let's use the formula for the sum of angles around a point. But if we assume that the figure is composed of angles around a point. Let's re - think.

Wait, actually, if we consider that the sum of angles around a point is \(360^{\circ}\). But if we assume that the angles are arranged such that we can use the property of vertical angles and linear pairs. Wait, a better approach: we know that \(c + 68^{\circ}+78^{\circ}+ \text{(other angles)}\). But if we assume that the figure is symmetric (by the nature of angle - around - a - point problems in basic geometry). Wait, no, another way.

We know that the sum of angles around a point is \(360^{\circ}\). But if we assume that the angles are in pairs (vertical angles). Wait, no, let's use the formula \(c+68^{\circ}+78^{\circ}+ \text{(angle equal to }c)+ \text{(angle equal to }68^{\circ})+\text{(angle equal to }78^{\circ})=360^{\circ}\). But a more straightforward way: if we consider that \(c + 68^{\circ}+78^{\circ}=180^{\circ}\) (assuming they are on a semi - circle).

Step2: Solve for \(c\)

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Answer:

\(34\)