Question

calculate the angles in degrees. do not try to measure, because the pictures are not exact. 1 angle aod = 2 angle aob =

Explanation:

Step1: Recall angle - sum property around a point

The sum of angles around a point is 360 degrees. In the first case, assume the right - angle at the intersection of OA and the vertical line is 90 degrees.

Step2: Calculate angle AOD for the first figure

We know that one angle is 67 degrees and another is 27 degrees. Also, considering the right - angle. Let $\angle AOD=x$. Then $x + 67+27+90 = 360$. First, add the known non - right angles: $67 + 27=94$. Then $x+94 + 90=360$. So $x=360-(94 + 90)=176$ degrees.

Step3: Calculate angle AOB for the second figure

The sum of angles around point O is 360 degrees. Let $\angle AOB = y$. We know two angles are 105 degrees and 50 degrees. Then $y+105 + 50=180$ (since they are on a straight - line, and the sum of angles on a straight - line is 180 degrees). So $y=180-(105 + 50)=25$ degrees.

Answer:

1. $\angle AOD = 176$ degrees
2. $\angle AOB = 25$ degrees