Table of Contents

Last modified on April 22nd, 2021

A right angle, also known as a 90-degree angle, is defined as an angle that measures exactly 90°. It is formed when two straight lines that are perpendicular to each other intersect at a point. A right angle is represented by the symbol ∟.

A few more right angles are shown below:

A 90-degree angle can be made by using only a scale and a compass. Follow the steps as shown below, to draw a 90-degree angle. Note that no protractor is used in any step of the process.

**Figure 3 – (Heading: How to Make a 90 Degree Angle Using a Compass, Filename – How to Make a 90 Degree Angle)**

- Geometric shapes such as square and rectangle have four right angles, a right trapezoid has two right angles, whereas a right angle triangle has one of its angle that is a right angle
- The two diagonals of some quadrilaterals such as a square, rhombus, or a kite intersect each other to form a right angle
- The angle formed by the hands of a clock showing 3’o clock and 9’ o clock
- Corners of square or rectangle-shaped swimming pools
- Corners of a paper, textbook, newspaper, and magazines
- Corners of a chessboard, table tennis board, ludo board, and billiard table
- Corners of a laptop and TV screen
- Corners of doors, windows, mirrors, and dinner table
- Corners of a Crossroad
- Corners of rooms in our homes, school, and offices
- The angle formed when a person is walking in relation to the ground
- Corners of each step of a staircase\

**Which of the following options given in the clock timing represents a right angle?**

Solution:

As we know,

Right angles are angles that measure 90°

Hence, options (a) and (b) are right angles.

**Find the missing angle x in the given triangle and state whether it is a right angle triangle**

Solution:

As we know,

The sum of the interior angles in a triangle is 180°,

Thus,

In △ABC,

∠ABC + ∠BCA + ∠CAB = 180°, here ∠CAB = 45°, ∠BCA = 45°

∠ABC + 45° + 45° = 180°

∠ABC = 180° – (45° + 45°)

∠ABC = (x°) = 90°

Since ∠ABC is 90°, △ABC is a right angle triangle

**Identify the right angles in the given quadrilateral ABCD. Given that ∠DAB and ∠ABC are equal.**

Solution:

As we know,

Sum of angles in a quadrilateral = 360°

Thus,

∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°, here, ∠BCD = 70°, ∠CDA = 110°

∠ABC + 70° + 110° + ∠DAB = 360°

∠ABC +∠DAB = 360° – (70° + 110°)

∠ABC +∠DAB = 180°

Now, since ∠ABC = ∠DAB,

2∠ABC = 180°

∠ABC = 90°

Also, ∠DAB = 90°

Thus, in the given trapezoid ∠ABC and ∠DAB are right angles. Also the quadrilateral ABCD is a right trapezoid.

**Ans**. Yes, for example a rhombus with four right angles is a square.

**Ans**. Yes, a parallelogram can have right angles as found in a square or a rectangle.

**Ans**. Yes, right trapezoid have right angles in them.

**Ans**. A square has four right angles.

**Ans**. No, all quadrilaterals for example a kite does not have right angles.

**Ans**. A pentagon can have a maximum of three right angles.

**Ans**. No, a triangle cannot have two right angles because the sum of the three angles in a triangle is 180°. If there are two right angles the measure of the third angles will be 0°, which is impossible.

**Ans**. A rectangle has four right angles.

Last modified on April 22nd, 2021