I need to solve the problem in the image, which asks to find the measure of the indicated angle in each linear pair. A linear pair consists of two adjacent angles that form a straight line, so their measures add up to 180 degrees.
I will go through each problem one by one, using the property that the sum of angles in a linear pair is 180°.
Let me start with problem 1:
- The diagram shows angle DOF and another angle measuring 114°.
- Since they form a linear pair, m∠DOF + 114° = 180°.
- Therefore, m∠DOF = 180° - 114° = 66°.
Now for problem 2:
- The diagram shows angle GOH and another angle measuring 106°.
- Since they form a linear pair, m∠GOH + 106° = 180°.
- Therefore, m∠GOH = 180° - 106° = 74°.
For problem 3:
- The diagram shows angle BOC and another angle measuring 136°.
- Since they form a linear pair, m∠BOC + 136° = 180°.
- Therefore, m∠BOC = 180° - 136° = 44°.
For problem 4:
- The diagram shows angle LON and another angle measuring x°.
- Since they form a linear pair, m∠LON + x° = 180°.
- Therefore, m∠LON = 180° - x°.
For problem 5:
- The diagram shows angle SOU and another angle measuring 17°.
- Since they form a linear pair, m∠SOU + 17° = 180°.
- Therefore, m∠SOU = 180° - 17° = 163°.
For problem 6:
- The diagram shows angle YOZ and another angle measuring 148°.
- Since they form a linear pair, m∠YOZ + 148° = 180°.
- Therefore, m∠YOZ = 180° - 148° = 32°.
For problem 7:
- The diagram shows angle ROS and another angle measuring 12°.
- Since they form a linear pair, m∠ROS + 12° = 180°.
- Therefore, m∠ROS = 180° - 12° = 168°.
For problem 8:
- The diagram shows angle UOW and another angle measuring 14°.
- Since they form a linear pair, m∠UOW + 14° = 180°.
- Therefore, m∠UOW = 180° - 14° = 166°.
I have now solved all the problems. Let me summarize the answers:
1) m∠DOF = 66°
2) m∠GOH = 74°
3) m∠BOC = 44°
4) m∠LON = 180° - x°
5) m∠SOU = 163°
6) m∠YOZ = 32°
7) m∠ROS = 168°
8) m∠UOW = 166°
Parent Tip: Review the logic above to help your child master the concept of pairs of angles worksheets.