Construct the following angles and verify by measuring them by a protractor:

(i) 75°


(ii) 105°


(iii) 135°



Steps of construction:


Step 1: Draw a ray OY.


Step 2: An arc BAE is drawn taking O as a centre.


Step3: With E as a centre, 2 arcs A and C are made on the arc BAE.


Step 4: Taking A and B as centre one by one, arcs are made to intersect at X and XOY = is drawn.


Step 5: Taking A and C as centres, arcs are made to intersect at D.


Step 6: OD is joined and hence, DOY = is constructed.


Thus, DOY is the required angle


(ii)


Steps of construction:


Step 1: Draw a ray OY.


Step 2: Taking O as a centre an arc ABC is drawn.


Step 3: With A as a centre, two arcs B and C are made on the arc ABC.


Step 4: Now, taking B and C as centres, arcs are made to intersect at E and EOY = 900is made.


Step 5: With B and C as centres, arcs are made to intersect at X.


Step 6: OX is joined and hence XOY = 1050 is constructed.


Thus, XOY is the required angle


(iii)


Steps of construction:


Step 1: A ray DY is drawn.


Step 2: An arc ACD is drawn with O as a centre.


Step 3: With A as a centre, two arcs B and C are made on the arc ACD.


Step 4: With B and C as centres, arcs are made to intersect at E and EOY = 900is made.


Step 5: With F and D as centres, arcs are made to intersect at X or bisector of angle EOD is constructed.


Step 6: OX is joined and XOY = 1350 is constructed.


Thus, XOY is the required angle


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