\( \square \) a a vertical angle measures \( 165.8^{\circ} \), what is the measure of its adjacent a. \( 4.2^{\circ} \) b. \( 24.2^{\circ} \) c. \( 14.2^{\circ} \) a. \( 46^{\circ} \) b. \( 56^{\circ} \) c. \( 26^{\circ} \)

When dealing with vertical angles, it's important to remember that they are equal. Therefore, if one vertical angle measures \( 165.8^{\circ} \), the other vertical angle will also measure \( 165.8^{\circ} \). Since adjacent angles form a straight line, their measures will add up to \( 180^{\circ} \). To find the measure of the adjacent angle, subtract \( 165.8^{\circ} \) from \( 180^{\circ} \): \[ 180^{\circ} - 165.8^{\circ} = 14.2^{\circ} \] So, the measure of the adjacent angle is \( 14.2^{\circ} \), making option c the correct choice. In real-world situations, understanding vertical angles can play a huge role in fields like architecture and engineering. For instance, if architects need to design a roof at a certain angle, they might use vertical angles to ensure that the structures meet properly at the apex. Knowing how to calculate these angles can save time and resources in construction tasks!