Angles of Rectangle
Angles of a rectangle are all right angles. A rectangle is a closed two-dimensional figure having four sides and four corners. It is characterized by two dimensions, its length, and width. The longer side of the rectangle is known as its length and the shorter side is known as its width.
|1.||What are Angles of Rectangle?|
|2.||Angles of Rectangle Properties|
|3.||Sum of Angles of Rectangle|
|4.||Diagonal Angles of Rectangle|
|5.||FAQs on Angles of Rectangle|
What are Angles of Rectangle?
A rectangle is a two-dimensional figure with four sides, four vertices, and four angles. Since a rectangle is a quadrilateral in which all four angles are equal to each other, the adjacent sides of a rectangle are meet at the right angle. Thus, the angle formed by its adjacent sides is 90°. The four sides of a rectangle are not equal but four angles are equal.
Angles of Rectangle Properties
Let's summarise the properties of angles of a rectangle as seen in the figure in the above section:
- There are four interior angles, each angle is a right angle.
- The sum of the interior angles of a rectangle is 360°.
- The adjacent angles of a rectangle are of equal measure.
- Any two consecutive angles of a rectangle are supplementary.
- The diagonal of a rectangle bisect each other but do not form right angles at the center.
Sum of Angles of Rectangle
We know that a rectangle is a quadrilateral only and as per the angle sum property of quadrilateral, the sum of all its interior angles is 360°. Also, we know that the four angles in a square, one at each vertex, are congruent. Thus, the interior angle of a rectangle at each vertex is 360°/4 = 90°. The interior angle of a rectangle at each vertex is 90°.
Diagonal Angles of Rectangle
The diagonals of a rectangle are of equal length and they bisect each other. The diagonals bisect each other but do not form right angles at the center. They form linear pairs of angles, obtuse angle + acute angle, as at each of the diagonal. The rectangle is called a square if its diagonals bisect each other at right angles as the diagonals of rectangle do not bisect the respective vertex angles into equal angles.
A diagonal divides a rectangle into two congruent triangles, that too right triangles with their hypotenuse being the same. Each diagonal acts as the hypotenuse for the right triangles so formed. Applying Pythagoras theorem to the triangle so formed, d2 = l2 + w2, where d is diagonal, l is length and w is the width of the rectangle. Taking square root on both sides, √(d2) = √( l2 + w2). Thus, the diagonal of a rectangle formula is: √(a² + b²).
- A square can also be referred to as a rectangle with two opposite sides having an equal length.
- The interior angles of a rectangle, as well as the square, are right angles.
- The length of the diagonals with sides a and b can be obtained using the Pythagoras theorem, diagonal d = √( a² + b²).
Examples on Angles of Rectangle
Example 1: ABCD is a rectangle. Find the angle x.
Given: Rectangle ABCD
Since triangle ABC is a right triangle, thus the sum of its three angles equal 180°.
⇒ 90° + (2x+20)° + (3x)° = 180° (Angle sum property)
⇒ 2x + 3x + 20 = 180 - 90
⇒ 5x = 90 - 20
⇒ x = 70/5 = 14°
Thus, (2x+20)° = 2 ×14 + 20 = 28 + 20 = 48°
(3x)° = 3 × 14 = 42°
Therefore, the measures of the two angles given as (2x+20)° and (3x)°are 48° and 42° respectively.
Example 2: Using properties of angles of the rectangle, find the diagonal of a rectangle whose dimensions are 6 units and 4 units.
Given: The dimensions of a rectangle = 6 units and 4 units.
According to the properties of angles of the rectangle, the diagonal of a rectangle = (d) = √( l2 + w2)
Length of diagonal of rectangle = √(6)2+(4)2 = √52 = 7.21 units.
Therefore, the length of the diagonal of the rectangle whose dimensions are 6 units and 4 units is 7.21 units.
FAQs on Angles of Rectangle
What Are the Angles of Rectangle in Geometry?
A rectangle has two pairs of equal opposite sides and four equal angles. The adjacent sides are perpendicular. Thus, a rectangle has four interior angles, each of which is equal to 90°.
What Are the 4 Angles of a Rectangle?
Since a rectangle has four angles of equal measure, the measure of each must be 360/4, or 90 degrees.
What Is the Sum of the Interior Angles of Rectangle?
A rectangle is a type of quadrilateral having both pairs of opposite sides equal. Thus, being a quadrilateral, the sum of its interior angles equals 360°.
What Type of Angles Does a Rectangle Have?
For a pair of opposite sides of a rectangle, the adjacent sides are transversals, which results in the property that the two consecutive angles are supplementary, that is, they add up to 180°.
How To Prove All Angles of a Rectangle Are 90 Degrees?
For a pair of opposite sides of a rectangle, their adjacent sides are transversals, which results in the property that the two consecutive angles are supplementary, that is, they add up to 180°. The opposite angles in any quadrilateral are non-adjacent angles formed by two intersecting lines and we know that the adjacent sides of a rectangle are perpendicular. Thus, the opposite angles of a rectangle are equal and measure 90°.
How To Find Diagonal Angles of a Rectangle?
The diagonals of a rectangle are equal in measure and bisect each other. The diagonals bisect each other but do not form right angles at the center. They form linear pairs of angles, obtuse angle + acute angle, as at each of the diagonal.