1. We are given a set of angle options: 10, 66, 165, 115, and 135 degrees. 2. To find possible mixes or matches, we might consider sums, differences, or relationships such as supplementary ($180^\circ$) or complementary ($90^\circ$) angles. 3. Check for supplementary pairs (angles that add to $180^\circ$): - $10 + 170 \neq 180$ (170 not in options) - $66 + 114 \neq 180$ (114 not in options) - $165 + 15 \neq 180$ (15 not in options) - $115 + 65 \neq 180$ (65 not in options) - $135 + 45 \neq 180$ (45 not in options) No pairs sum to exactly $180^\circ$ from the given options. 4. Check if any pairs sum to $90^\circ$: None do. 5. Given the options, the angles themselves are the possible choices for mix and match as no special complementary or supplementary relationships are seen directly. 6. Thus, the possible angles to use are $10^\circ, 66^\circ, 165^\circ, 115^\circ,$ and $135^\circ$.