Constructing a 135-degree angle using a compass and ruler is a fundamental exercise in geometry that builds on the knowledge of constructing basic angles. To achieve this, you first need to construct a 90-degree angle, which is a right angle, and then add a 45-degree angle to it. In this article, we will discuss the construction of an angle of 135 degrees.

Angle Construction in Geometry

Angle construction in geometry is a fundamental skill that involves creating specific angles using basic tools such as a compass, ruler, and protractor. This process is crucial for developing an understanding of geometric principles and for solving various mathematical problems.

Basic Tools Required

• Compass: Used for drawing arcs and circles.
• Ruler: For drawing straight lines.
• Protractor: Helps in measuring and drawing specific angles.
• Pencil: For marking points and drawing lines.

Steps to Construct a 135-Degree Angle

Step 1: Draw a straight line and label it AB.

Step 2: Place the compass point on point A & draw an arc that crosses AB at some point, label it CD by extending the AB line.

Step 3: Without changing the compass width, place the compass point on C & draw another arc above AB, creating an intersection point, label it E.

Step 4: Without changing the compass width, from point E, create another arc on arc CD & mark it F.

Step 5: Now from point E & F, create another arc above arc CD & mark their intersection as G.

Step 6: Now through point A create a straight line joining point G & A. Mark the point on arc CD as H through which the FA line is passing.

Step 7: Now from point G & D create arcs that intersects at I.

Step 8: Meet AI to form 135 degree angle.

Result: ∠HAD is 135°.

Read More,

• Geometry
• Contruction of Triangle
• nstruction of Similar Triangles
• Worksheet on Constructions of Triangles

FAQs on Construction of 135 Degree Angle

What tools do I need to construct a 135-degree angle?

You will need a compass, a ruler, a protractor (optional for verification), and a pencil to construct a 135-degree angle.

Can I verify the constructed 135-degree angle using a protractor?

Yes, after constructing the angle using a compass and ruler, you can use a protractor to measure the angle to ensure it is exactly 135 degrees.

Is it possible to construct a 135-degree angle without a protractor?

Yes, you can construct a 135-degree angle without a protractor by accurately using a compass and ruler.

What are some common mistakes to avoid when constructing angles?

Some common mistakes to avoid are:

• Not keeping the compass width consistent when drawing arcs.
• Incorrectly marking points and intersections.
• Not extending lines accurately through intersection points.