Question

sept. 3 unit 1 #9 the student be able to calculate missing angles in a figure
1 find the measure of angle aob.
2 find the measure of angle cod.
3 find the measure of angle eod.
4 find the measure of angle boc.
5 find the measure of angle doe.
6 find the measure of angle aob.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. Adjacent angles on a straight - line sum to 180 degrees.

Step2: For the first set of angles

1. Angle AOB and the 38 - degree angle are vertical angles. So, $\angle AOB = 38^{\circ}$.
2. Angle COD and the 45 - degree angle are vertical angles. So, $\angle COD=45^{\circ}$.
3. Angle EOD and the 38 - degree angle are adjacent on a straight - line. So, $\angle EOD = 180^{\circ}-38^{\circ}=142^{\circ}$.

Step3: For the second set of angles

1. Angle BOC and the 50 - degree angle are vertical angles. So, $\angle BOC = 50^{\circ}$.
2. Angle DOE and the 130 - degree angle are vertical angles. So, $\angle DOE = 130^{\circ}$.
3. Angle AOB and the 130 - degree angle are adjacent on a straight - line. So, $\angle AOB=180^{\circ}-130^{\circ}=50^{\circ}$.

Answer:

1. $\angle AOB = 38^{\circ}$
2. $\angle COD = 45^{\circ}$
3. $\angle EOD = 142^{\circ}$
4. $\angle BOC = 50^{\circ}$
5. $\angle DOE = 130^{\circ}$
6. $\angle AOB = 50^{\circ}$