Question

in the diagram, which two angles must be supplementary with angle 6?
∠5 and ∠7
∠1 and ∠10
∠14 and ∠16
∠7 and ∠11

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\). In a diagram with intersecting lines, adjacent angles on a straight line are supplementary.

Step2: Analyze the relationship of \(\angle6\) with other angles

For \(\angle6\), \(\angle5\) and \(\angle6\) form a linear - pair (adjacent angles on a straight line), so \(\angle5+\angle6 = 180^{\circ}\). Also, \(\angle7\) and \(\angle6\) form a linear - pair (because of the intersecting lines), so \(\angle7+\angle6=180^{\circ}\)

Answer:

\(\angle5\) and \(\angle7\)