Question

7 consider the figure shown below. match the angles given in the first column with their equivalent degree
angles 65° 75° 115° 105°
∠3
∠8
∠6
∠11
∠9
∠4

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1 = 65^{\circ}$, and $\angle3$ is vertical to $\angle1$, so $\angle3=65^{\circ}$.

Step2: Use corresponding - angle property

$\angle5 = 75^{\circ}$, and $\angle8$ is corresponding to $\angle5$, so $\angle8 = 75^{\circ}$.

Step3: Use vertical - angle property for $\angle6$

$\angle6$ is vertical to $\angle5$, so $\angle6=75^{\circ}$.

Step4: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. $\angle1 = 65^{\circ}$, so $\angle2=180 - 65=115^{\circ}$. $\angle11$ is vertical to $\angle2$, so $\angle11 = 115^{\circ}$.

Step5: Use linear - pair and vertical - angle properties for $\angle9$

$\angle5$ and $\angle9$ are same - side interior angles. $\angle5 = 75^{\circ}$, and the angle adjacent to $\angle9$ (vertical to $\angle5$) is $75^{\circ}$. So $\angle9=105^{\circ}$.

Step6: Use vertical - angle property for $\angle4$

$\angle4$ is vertical to $\angle2$, so $\angle4 = 115^{\circ}$.

Answer:

$\angle3:65^{\circ}$
$\angle8:75^{\circ}$
$\angle6:75^{\circ}$
$\angle11:115^{\circ}$
$\angle9:105^{\circ}$
$\angle4:115^{\circ}$