Question

which angles are supplementary to $\angle 14$? select all that apply.

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles that add up to \(180^{\circ}\). Angles that form a linear - pair (adjacent angles on a straight line) are supplementary. Also, vertical angles and angle - relationships in parallel - line and transversal setups can be used.

Step2: Analyze the relationship of \(\angle14\) with other angles

• \(\angle14\) and \(\angle13\): They form a linear - pair (adjacent angles on a straight line). So, \(\angle14+\angle13 = 180^{\circ}\).
• \(\angle14\) and \(\angle16\): They form a linear - pair (adjacent angles on a straight line). But since \(\angle16\) is not in the options, we look for angles equal to \(\angle16\) (using vertical or corresponding angles).
• \(\angle14\) and \(\angle10\): \(\angle14\) and \(\angle16\) are a linear - pair. \(\angle16\) and \(\angle10\) are corresponding angles (assuming parallel lines and transversal). So, \(\angle14+\angle10=180^{\circ}\) (because \(\angle14 + \angle16=180^{\circ}\) and \(\angle16=\angle10\)).
• \(\angle14\) and \(\angle9\): \(\angle14\) and \(\angle16\) are a linear - pair. \(\angle16\) and \(\angle9\) are vertical angles. So, \(\angle14+\angle9 = 180^{\circ}\) (because \(\angle14+\angle16 = 180^{\circ}\) and \(\angle16=\angle9\)).
• \(\angle14\) and \(\angle11\): \(\angle14\) and \(\angle11\) are not supplementary. \(\angle14\) and \(\angle13\) are supplementary, and \(\angle11\) and \(\angle13\) are vertical angles. If \(\angle14+\angle13 = 180^{\circ}\) and \(\angle11=\angle13\), then \(\angle14+\angle11

eq180^{\circ}\) (it's a wrong assumption from the initial look at the figure's structure).

Answer:

\(\angle9\), \(\angle10\), \(\angle13\)