To determine which pair of angles has congruent values for [tex]\(\sin x^{\circ}\)[/tex] and [tex]\(\cos y^{\circ}\)[/tex], let's evaluate each pair individually.
1. Pair: [tex]\(70^{\circ}\)[/tex] and [tex]\(160^{\circ}\)[/tex]
- [tex]\(\sin(70^{\circ}) \approx 0.9397\)[/tex]
- [tex]\(\cos(160^{\circ}) \approx -0.9397\)[/tex]
2. Pair: [tex]\(70^{\circ}\)[/tex] and [tex]\(70^{\circ}\)[/tex]
- [tex]\(\sin(70^{\circ}) \approx 0.9397\)[/tex]
- [tex]\(\cos(70^{\circ}) \approx 0.3420\)[/tex]
3. Pair: [tex]\(70^{\circ}\)[/tex] and [tex]\(120^{\circ}\)[/tex]
- [tex]\(\sin(70^{\circ}) \approx 0.9397\)[/tex]
- [tex]\(\cos(120^{\circ}) \approx -0.5000\)[/tex]
4. Pair: [tex]\(70^{\circ}\)[/tex] and [tex]\(20^{\circ}\)[/tex]
- [tex]\(\sin(70^{\circ}) \approx 0.9397\)[/tex]
- [tex]\(\cos(20^{\circ}) \approx 0.9397\)[/tex]
Therefore, the pair of angles that have congruent values for [tex]\(\sin x^{\circ}\)[/tex] and [tex]\(\cos y^{\circ}\)[/tex] is the pair [tex]\(70^{\circ}\)[/tex] and [tex]\(20^{\circ}\)[/tex].
