LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

CONSTRUCTION OF 135⁰ ANGLE

__CONSTRUCTION OF 135 DEGREE (135⁰) ANGLE -__

**construct a 135-degree angle using a compass and straightedge, you can follow these steps:**

__Draw a base line:-__Start by drawing a straight line, which will be the base for your angle.**Place the compass at one endpoint: Place the compass point (the sharp end) on one endpoint of the base line.**__Adjust the compass width:-__Open the compass to a width greater than half the length of the base line. This will ensure that the arc you draw will intersect the base line on both sides.__Draw an arc:-__With the compass set, draw an arc that intersects the base line.__Place the compass at the intersection point:-__Place the compass point at the intersection point you just created on the base line.__Draw another arc:-__Without changing the compass width, draw another arc from the intersection point.__Draw the angle bisector:-__The intersection of the two arcs should form an angle bisector. Draw a straight line from the initial endpoint through the intersection point to the other side of the base line.__Measure the angle:-__The angle formed by the intersection of the base line and the bisector is 135 degrees.

**This construction uses the properties of angles and bisectors to create a 135-degree angle. Make sure to use a ruler to draw straight lines and a compass to create accurate arcs.**

__Another Way Of Construction -__

**Steps Of Construction -**

__Step.1)__ Draw any straight line BA, and take a point O on it.

__Step.2)__ With O as centre and suitable radius, draw an arc to cut the line.

__Step.3)__ With B & A as centres, draw two arc of equal radius (>1/2 BA) cutting each other at C.

__Step.4)__ Construct ∠COA = 90⁰, then ∠BOC = 90⁰.

__Step.6)__ Bisect ∠BOC. Let ray OD be the bisector of ∠BOC, then ∠COD = 45⁰

**So, ∠AOD = ∠AOC + ∠COD**

** = 90⁰ + 45⁰ = 135⁰**