## Trigonometry (10th Edition)

$\angle1,\angle9,\angle10=55^{\circ}$ $\angle2,\angle4=65^{\circ}$ $\angle3,\angle5,\angle7,\angle8=60^{\circ}$ $\angle6=120^{\circ}$
1. We will find angles in not numerical order. The easiest way is to start from finding vertical angles of labeled angles (two intersecting lines and angles opposite each other) $\angle6=120^{\circ}$ and $\angle1=55^{\circ}$ 2. Angle 8 and angle labeled 120 degrees make up a straight line, so they must add up to 180 degrees, therefore: $\angle8=180^{\circ}-120^{\circ}=60^{\circ}$ 3. Angle 7 and 8 are vertical, therefore congruent $\angle7=\angle8=60^{\circ}$ 4. Angle 10 is an alternate interior angle with the angle labeled 55 degrees $\angle10=55^{\circ}$ 5. Angles 9 and 10 are vertical angles therefore $\angle9=\angle10=55^{\circ}$ 6. Angles 5 and 8 are corresponding angles $\angle5=\angle8=60^{\circ}$ 7. Angles 3 and 5 are vertical $\angle3=\angle5=60^{\circ}$ 8. Angle 4 makes a straight line with angles 5, and labeled 55, so they must add up to 180'degrees. $\angle4= 180-60-55=65^{\circ}$ 9. Also $\angle2=\angle4=65^{\circ}$