Question

1. in the polygon pictured, which angles are supplementary?

c° and d°
a° and k°
g° and f°
c° and i°

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze each option

• For \(c^{\circ}\) and \(d^{\circ}\): They are adjacent angles around a point on a straight - line. But in the context of the polygon (assuming the lines are straight), \(c + d=360^{\circ}\) (a full - circle around a point), not \(180^{\circ}\).
• For \(a^{\circ}\) and \(k^{\circ}\): There is no information to suggest they are on a straight - line or their sum is \(180^{\circ}\).
• For \(g^{\circ}\) and \(f^{\circ}\): These two angles form a linear pair (they are adjacent and their non - common sides form a straight - line). So, \(g + f=180^{\circ}\) (by the definition of a linear pair of angles).
• For \(c^{\circ}\) and \(i^{\circ}\): There is no geometric relationship (like being on a straight - line) that would make their sum \(180^{\circ}\).

Answer:

\(g^{\circ}\) and \(f^{\circ}\)