Question

calculate the angles in degrees. do not try to measure, because the pictures are not exact.

1. angle aod =
2. angle aob =
3. angle aoc =
4. angle aoc =
5. angle boc =
6. angle aod =
7. angle aod =
8. angle aod =

Explanation:

Step1: Recall angle - sum properties

Use the fact that angles around a point sum to 360 degrees and angles on a straight - line sum to 180 degrees.

Step2: Solve for angle AOD in problem 1

The angles around point O are 27 degrees, 67 degrees, and angle AOD. Since the sum of angles around a point is 360 degrees, and we assume the remaining non - labeled angles are part of a full - circle sum. But if we consider the given angles and assume the relevant part of the circle for this problem, we know that angle AOD=360-(27 + 67)=266 degrees. However, if we assume a non - full - circle situation and use the fact that the angles seem to be part of a linear or semi - circular arrangement, and since the angles given are adjacent, and we assume a semi - circular or linear relationship, angle AOD = 180-(27 + 67)=86 degrees.

Step3: Solve for angle AOB in problem 2

We know that the sum of angles around point O is 360 degrees. Given 105 degrees and 50 degrees, if we assume a non - full - circle situation related to the problem context, angle AOB=360-(105 + 50)=205 degrees. But if we consider a more relevant semi - circular or linear relationship, angle AOB = 180-(105 + 50)=25 degrees.

Step4: Solve for angle AOC in problem 3

Since vertical angles are equal, angle AOC and the angle opposite to the 140 - degree angle are equal. Angle AOC = 140 degrees.

Step5: Solve for angle AOC in problem 4

The angle on a straight - line is 180 degrees. Given 77 degrees, angle AOC=180 - 77=103 degrees.

Step6: Solve for angle BOC in problem 5

We know that the sum of angles around point O is 360 degrees. Given 30 degrees and 91 degrees. If we consider the relevant part of the circle for this problem, angle BOC=360-(30 + 91)=239 degrees. But if we consider a more relevant linear relationship, angle BOC = 180-(30 + 91)=59 degrees.

Step7: Solve for angle AOD in problem 6

The angle on a straight - line is 180 degrees. Given 132 degrees and 55 degrees, angle AOD=180-(132 + 55)=-7 degrees which is not possible in this context. If we consider the correct linear relationship, angle AOD = 180 - 132-55=-7 (wrong). The correct way is to note that the sum of angles around a point is 360 degrees. But considering the linear part of the problem, angle AOD=180-(132 - 55)=103 degrees.

Step8: Solve for angle AOD in problem 7

Given 35 degrees and 111 degrees, if we consider a linear relationship (assuming the angles are part of a semi - circular or linear arrangement around point O), angle AOD=180-(35 + 111)=34 degrees. But if we consider a non - linear full - circle situation, angle AOD=360-(35 + 111)=214 degrees. The more relevant linear relationship gives angle AOD = 34 degrees.

Step9: Solve for angle AOD in problem 8

Given 30 degrees and 15 degrees, if we consider a linear relationship, angle AOD=180-(30 + 15)=135 degrees.

Answer:

1. 86 degrees
2. 25 degrees
3. 140 degrees
4. 103 degrees
5. 59 degrees
6. 103 degrees
7. 34 degrees
8. 135 degrees