ABCD is a parallelogram where AO and BO bisect angles A and angle B respectively. What is the measure of ∠AOB?
What's the answer? Thanks!!!! :)
Since the diagonals bisect the angles, the figure is a rhombus, whose diagonals are perpendicular.
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To find the measure of angle AOB, we need to use the properties of a parallelogram and the fact that AO and BO bisect angles A and B, respectively.
1. In a parallelogram, opposite angles are equal. This means that angles A and C are equal, and angles B and D are equal.
2. Since AO and BO bisect angles A and B, respectively, it means that angles OAB and OBA are equal.
3. Let's denote the measure of angle AOB as x.
4. Since angles A and B are equal (opposite angles in a parallelogram), angle A must be (180 - x) degrees and angle B must also be (180 - x) degrees.
5. In triangle AOB, the sum of the angle measures must be 180 degrees. Therefore, we can write the equation as follows:
(180 - x) + (180 - x) + x = 180
6. Simplify the equation:
360 - 2x + x = 180
360 - x = 180
-x = -180
x = 180
Therefore, the measure of angle AOB is 180 degrees.
Explanation of how to find the answer:
To find the measure of angle AOB, we used the properties of a parallelogram (opposite angles are equal) and the fact that AO and BO bisect angles A and B, respectively. By setting up an equation and solving for x, we determined that the measure of angle AOB is 180 degrees.