45-degree angle - Definition with Examples

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45-Degree Angle

When two rays intersect at a common endpoint, they form an angle. The common endpoint is called the vertex, and the rays are called the arms of the angle.

45-Degree Angle


An angle is measured in° or radians. If the two arms of an angle extend in exactly opposite directions, it is a straight angle. A straight angle measures 180°. An angle can be measured using a protractor, and the angle of measure 90 degrees is called a right angle. In a right angle, the two arms are perpendicular to each other. 

right angle


When the right angle is divided into two equal parts each angle measures 45°.

divide right angle


Constructing a angle using a protractor 

Step 1: Draw a ray and name it AB.

Draw ray


Step 2: Keep the center point of the protractor at A. Since the angle opens to the right, choose 45° in the list that starts at the right and moves in the anticlockwise direction. Mark the point C.



Step 3: Join A and C. Here, measures .

divide right angle


45 Degree Angles in Real Life:

  • Symmetric windows

  • Based on the location and climate of the place, some solar panels are installed at an angle of 45° for optimal solar energy production

45-degree angles in real life


Additional Knowledge:

Constructing a angle using a compass

Step 1: Draw a line segment  and the perpendicular bisector of  by intersecting the arcs of radius more than half of the length MN. Let the perpendicular bisector intersect the line segment  at O.


line segment


Step 2: Draw an arc centered at O with a radius OM, cutting the perpendicular bisector at P.

arc centered


Step 3: Join M and P using a straight line. measures .

angular bisector

An angle of measure  degree can also be constructed by constructing the angular bisector of a right angle.

  Fun Facts

  • The diagonals of a square make an angle of measure  with the sides.

  • If one acute angle of an isosceles right triangle measures , so is the other.


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