Question

"Question 6 Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Understanding Quadrilaterals Page 51"

Answer 1

Let ABCD be a parallelogram.
Sum of adjacent angles of a parallelogram = 180°
∠A + ∠B = 180°
⇒ 2∠A = 180°
⇒ ∠A = 90°
also, 90° + ∠B = 180°
⇒ ∠B = 180° - 90° = 90°
∠A = ∠C = 90°
∠B = ∠D = 90°

Answer 2

The measure of each of the angles of the parallelogram is 90°.

• A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
• A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides. The qualities of a parallelogram are shared by the shapes of a square and a rectangle.
• A parallelogram is a rhombus if all of its sides are equal to one another or congruent. A trapezium is a shape that has one parallel side and two non-parallel sides.

Here, according to the given information, we are given that,

Two adjacent angles of a parallelogram have equal measure.

Now, we know that, in a parallelogram, the adjacent angles sum to make 180 degrees.

If x and y are the two adjacent angles,

Then, $x = y$ and we have,

$x+y=180.$

Or, $2x=180$

Or, $x = 90.$

Now, this means that, the other angles which are adjacent angles are equal and each angle is 90 degrees since the sum of the interior angles is 360 degrees.

Hence, the measure of each of the angles of the parallelogram is 90°.

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