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Using ruler and compasses only, draw an angle of measure of $135^{\circ}$ and choose which angle is this,

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Right angle

Obtuse angle

Acute angle

none

answer is B.

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Detailed Solution

To draw the angle of measure of

135^{\circ}

follow the below steps.
Step 1- Make a line

AB

. On this line make a point

O

.
Step 2- Now let this point O is centre. Make an arc

P Q

with some measure of radius by using the compass which intersect the line segment

AB

at the point

P

and

Q

.
Step 3- Now keep the value of radius same, make another arc from point P which intersect arc

PQ

at the point R.
Step 4- Similarly, plot another arc from point Q with same radius which intersect arc

PQ

at the point

S

, opposite to the point

P

.
Step 5- Now with points

S

and

R

draw two arcs of radius greater than ½ of

SR

, which intersect each other at point

T

. Make line from

O

T

which intersect the arc

PQ

at the point

C

.
Step 6 –Now with

C

and

Q

points make another two arc with radius greater than ½ of

CQ

, which intersect each other at point D. make a line from

O

D

and extend this line OD to the point

X

which makes ray

OX

Here, the measure of

∠ AOX

135^{\circ}

.
Now as the measure of angle is more than 90 degrees. Thus, it is an obtuse angle.
Correct option is 2.

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Using ruler and compasses only, draw an angle of measure of 135∘ and choose which angle is this,

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Using ruler and compasses only, draw an angle of measure of $135^{\circ}$ and choose which angle is this,