Question

One angle of a parallelogram is measure 75 degree find the measures of the remaining angles

Answer 1

Given - Angle of parallelogram = 75°

Find - Measure of remaining angles

Solution - As per the fact, the opposite angles of parallelogram are equal. So, two angles will be 75° each.

Now finding the remaining two angles. The angles on the same line will sum up to 180°.

Let us say angle A and angle D are opposite angles. So, angle A and angle D is 75°.

Now, sum of angle A and angle B or sum of angle A and angle C will be 180°.

Thus, angle A + angle B = 180°

75 + angle B = 180

Angle B = 105°

As angle B and angle C are opposite angles, it is also 105°.

So, the remaining angles of parallelogram are 75°, 105° and 105°.

Answer 2

Given: One angle of a parallelogram is measure 75 degree.

To find: The measures of the remaining angles.

Solution:

In a parallelogram, just like the sides, the opposite angles are also the same. Also, in a parallelogram, the adjacent angles are supplementary to one another. Let the vertices of the parallelogram be A, B, C and D.

If ∠A is 75 degrees, then the measure of ∠C must also be 75 degrees. Now, the sum of the measures of ∠A and ∠B is supposed to be equal to 180 degrees.

$\angle A + \angle B = 180$

$75 + \angle B = 180$

$\angle B = 105$

Similarly, if ∠B is 105 degrees, then the measure of ∠D must also be 105 degrees.

Therefore, the measures of the remaining angles are 75, 105 and 105.