Question

Construct a angle of 110' ?

Answer 1

1) Initially construct a horizontal line.
2) Mark a point A on it. with A as center and any suitable radius draw a semi circular arc. Which intersect the horizontal line at two distinct points, say $P\&Q$.
3) With Q as center and with the same radius as in (2) above, cut an arc at R on the semic circle. Joint A-R; So $\angle QAR=60deg$
4) At a below PQ, draw an inclined line, perferably it subtends an acute angle with AQ. On this invlinrf linr, mark 6 equal divisions using compass starting from A. Let these points be marked as 1,2,3,4, 5 & 6. Join 6th point with Q. Then through the points 1,2,3,4 & 5 draw parallel lines to intersect AQ at 5 distinct points. Say A1, A2, A3, etc.,
5) Through these point of intersection on AQ, draw lines parallel to AR to intersect the are QR at five different points, say Q1, Q2, Q3, etc..
6) Join $A-Q_1,A-Q_2,A-Q_3\Rightarrow \angle QA{Q}_1=10deg;\angle QA{Q}_2=20deg;\angle AQ{Q}_3=30deg$etc.
7) One arc length between successive points can be measured with compass, and any number of arcs from point. R can be cut off. Every successive points make 10deg. Thus for 110 deg. from R we need 5 successive divisions. Then join the 5tgh (say S) with A, making $\angle QAS=110deg$
8) Similar to the above any required angle can be marked.
9) For 85 deg. mark 80 and 90 angle. Using compass, bisect this arc, which will give 85 deg