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1 angle aod = 2 angle aob = 3 angle aoc = 4 angle aoc = 5 angle boc = 6…

Question

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: Use vertical - angle or angle - addition rules

  1. In the first figure:
  • We know that the sum of angles around a point is 360°. If we assume the vertical - angle relationship and angle - addition. Let's assume the angles are related as follows. Angle AOD: The sum of the given angles around point O should be considered. If we assume the vertical - angle and supplementary - angle relationships. We know that a full - circle is 360°. But if we consider the straight - line property (a straight - line is 180°), and assume the given angles, we find that angle AOD = 180°-(67° + 27°)=86°.
  1. In the second figure:
  • Angle AOB: We know that the sum of angles around a point is 360°. Using the fact that vertical angles are equal and angle - addition. Angle AOB = 360°-(105° + 50° + 90°)=115°.
  1. In the third figure:
  • Since vertical angles are equal, angle AOC and angle BOD are vertical angles. Given angle BOD = 140°, so angle AOC = 140°.
  1. In the fourth figure:
  • Angle AOC: Since the angle on a straight - line is 180°, and given angle BOC = 77°, then angle AOC = 180° - 77°=103°.
  1. In the fifth figure:
  • Angle BOC: We know that angle AOD = 180° (a straight - line). Given angle AOB = 30° and angle COD = 91°. Then angle BOC=180°-(30° + 91°)=59°.
  1. In the sixth figure:
  • Angle AOD: We know that the sum of angles around a point is 360°. Angle AOD = 360°-(132°+55° + 90°)=83°.
  1. In the seventh figure:
  • Angle AOD: We know that the sum of angles around a point is 360°. First, find the non - given angle adjacent to 111° and 35°. Let the non - given angle be x. x = 180° - 111°=69°. Then angle AOD = 180°-(35°+69°)=76°.
  1. In the eighth figure:
  • Angle AOD: We know that the sum of angles around a point is 360°. First, find the non - given angle adjacent to 30° and 15°. Let the non - given angle be y. y = 180°-(30° + 15°)=135°. Then angle AOD = 135°.

Answer:

  1. 86°
  2. 115°
  3. 140°
  4. 103°
  5. 59°
  6. 83°
  7. 76°
  8. 135°