Question
Using ruler and compasses only, draw an angle of measure 135°.
✓
Answer
We draw a line AB and mark a point O on it.
With a convenient radius and centre at O, draw an arc PQ with the help of a compass intersecting the line AB at P and Q.
With the same radius and centre at P, draw another arc intersecting the arc PQ at R.
With the same radius and centre at Q, draw one more arc intersecting the arc PQ at S, opposite to P.
Taking S and R as centres and radius more than half of SR, draw two arcs intersecting each other at T.
Join O and T intersecting the arc PQ at C.
Taking C and Q as centres and radius more than half of CQ, draw two arcs intersecting each other at D.
Join O and D and extend it to X to form the ray OX.
$\angle\text{AOX}$ is the required angle of measure 135°.
With a convenient radius and centre at O, draw an arc PQ with the help of a compass intersecting the line AB at P and Q.
With the same radius and centre at P, draw another arc intersecting the arc PQ at R.
With the same radius and centre at Q, draw one more arc intersecting the arc PQ at S, opposite to P.
Taking S and R as centres and radius more than half of SR, draw two arcs intersecting each other at T.
Join O and T intersecting the arc PQ at C.
Taking C and Q as centres and radius more than half of CQ, draw two arcs intersecting each other at D.
Join O and D and extend it to X to form the ray OX.
$\angle\text{AOX}$ is the required angle of measure 135°.
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