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=)_

Explanation:

Step1: Use vertical - angle property

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

Step2: Use corresponding - angle property

$\angle5$ and the $72^{\circ}$ angle are corresponding angles. Since $a\parallel b$, $m\angle5=72^{\circ}$.

Step3: Use linear - pair property

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

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 the $155^{\circ}$ angle are corresponding angles. Since $a\parallel b$, $m\angle3 = 155^{\circ}$.

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

$\angle7$ and $\angle3$ are vertical angles, so $m\angle7 = 155^{\circ}$.

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

$\angle4$ and the $25^{\circ}$ angle are vertical angles, so $m\angle4 = 25^{\circ}$.

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

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

Answer:

1. $m\angle1 = 72^{\circ}$
2. $m\angle5 = 72^{\circ}$
3. $m\angle2 = 108^{\circ}$
4. $m\angle6 = 108^{\circ}$
5. $m\angle3 = 155^{\circ}$
6. $m\angle7 = 155^{\circ}$
7. $m\angle4 = 25^{\circ}$
8. $m\angle8 = 108^{\circ}$