The angle between two altitudes of a Parallelogram through the vertex of an obtuse angle of the Parallelogram of 60∘. Find the angles of the Parallelogram

To find the angles of the parallelogram, we need to use the given information about the angle between two altitudes through the vertex of an obtuse angle, which is 60 degrees.

Step 1: Recall that the opposite angles of a parallelogram are equal. Therefore, the opposite angle to the given obtuse angle is also 60 degrees.

Step 2: Since the sum of the angles in a parallelogram is 360 degrees, we can find the measure of the other two angles by subtracting the known angles from 360.

Step 3: Let's denote the measure of one of the remaining angles as x. Since the opposite angle is also x, we can write the equation: x + x + 60 + 60 = 360.

Step 4: Simplifying the equation, we have: 2x + 120 = 360.

Step 5: Subtracting 120 from both sides, we get: 2x = 240.

Step 6: Dividing both sides by 2, we find: x = 120.

Step 7: Therefore, the measure of each of the remaining angles is 120 degrees.

In conclusion, the angles of the parallelogram are: 60 degrees, 60 degrees, 120 degrees, and 120 degrees.