Question

parallel lines a and b, when cut by transversal l, form eight angles, as shown in the diagram below. find the measure of each of the angles. (dok 2)

1. (mangle1=)
2. (mangle5=)
3. (mangle2=)
4. (mangle6=)
5. (mangle3=)
6. (mangle7=)
7. (mangle4=)
8. (mangle8=)

parallel lines a and b, when cut by transversal l, form eight angles, as shown in the diagram below. find the measure of each of the angles. (dok 2)

1. (mangle1=)
2. (mangle5=)
3. (mangle2=)
4. (mangle6=)
5. (mangle3=)
6. (mangle7=)
7. (mangle4=)
8. (mangle8=)

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. For the first diagram: $\angle1$ and the given $72^{\circ}$ angle are vertical angles, so $m\angle1 = 72^{\circ}$.

Step2: Use corresponding - angle property

Corresponding angles formed by parallel lines and a transversal are equal. $\angle5$ and the given $72^{\circ}$ angle are corresponding angles, so $m\angle5=72^{\circ}$.

Step3: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair (sum to $180^{\circ}$). So $m\angle2 = 180 - 72=108^{\circ}$.

Step4: Use vertical - angle property for $\angle6$

$\angle6$ and $\angle2$ are vertical angles, so $m\angle6 = 108^{\circ}$.

Step5: Use corresponding - angle property for $\angle3$

$\angle3$ and $\angle2$ are corresponding angles, so $m\angle3 = 108^{\circ}$.

Step6: Use vertical - angle property for $\angle7$

$\angle7$ and $\angle3$ are vertical angles, so $m\angle7 = 108^{\circ}$.

Step7: Use vertical - angle property for $\angle4$

$\angle4$ and the given $108^{\circ}$ angle are vertical angles, so $m\angle4 = 108^{\circ}$.

Step8: Use vertical - angle property for $\angle8$

$\angle8$ and $\angle4$ are vertical angles, so $m\angle8 = 108^{\circ}$.

For the second diagram:

Step9: Use vertical - angle property

$\angle1$ and the given $63^{\circ}$ angle are vertical angles, so $m\angle1 = 63^{\circ}$.

Step10: Use corresponding - angle property

$\angle5$ and the given $63^{\circ}$ angle are corresponding angles, so $m\angle5 = 63^{\circ}$.

Step11: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. So $m\angle2=180 - 63 = 117^{\circ}$.

Step12: Use vertical - angle property for $\angle6$

$\angle6$ and $\angle2$ are vertical angles, so $m\angle6 = 117^{\circ}$.

Step13: Use corresponding - angle property for $\angle3$

$\angle3$ and $\angle2$ are corresponding angles, so $m\angle3 = 117^{\circ}$.

Step14: Use vertical - angle property for $\angle7$

$\angle7$ and $\angle3$ are vertical angles, so $m\angle7 = 117^{\circ}$.

Step15: Use vertical - angle property for $\angle4$

$\angle4$ and the given $117^{\circ}$ angle are vertical angles, so $m\angle4 = 117^{\circ}$.

Step16: Use vertical - angle property for $\angle8$

$\angle8$ and $\angle4$ are vertical angles, so $m\angle8 = 117^{\circ}$.

Answer:

1. $m\angle1 = 72^{\circ}$
2. $m\angle5 = 72^{\circ}$
3. $m\angle2 = 108^{\circ}$
4. $m\angle6 = 108^{\circ}$
5. $m\angle3 = 108^{\circ}$
6. $m\angle7 = 108^{\circ}$
7. $m\angle4 = 108^{\circ}$
8. $m\angle8 = 108^{\circ}$
9. $m\angle1 = 63^{\circ}$
10. $m\angle5 = 63^{\circ}$
11. $m\angle2 = 117^{\circ}$
12. $m\angle6 = 117^{\circ}$
13. $m\angle3 = 117^{\circ}$
14. $m\angle7 = 117^{\circ}$
15. $m\angle4 = 117^{\circ}$
16. $m\angle8 = 117^{\circ}$