Question

Construct the following angles and verify by measuring them by a protractor
4
0 75°
(ii) 105°
truct an equilateral triangle given it
( 135​

Answer 1

Answer:

Step-by-step explanation:

(i) 75°

Steps of constructions:

Step 1: A ray OY is drawn.

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

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

Step 4: With A and B as centres, arcs are made to intersect at X and ∠XOY = 90° is made.

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

Step 6: OD is joined and and ∠DOY = 75° is constructed.

Thus, ∠DOY is the required angle making 75° with OY.

(ii) 105°

Steps of constructions:

Step 1: A ray OY is drawn.

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

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

Step 4: With B and C as centres, arcs are made to intersect at E and ∠EOY = 90° is made.

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

Step 6: OX is joined and and ∠XOY = 105° is constructed.

Thus, ∠XOY is the required angle making 105° with OY.

(iii) 135°

Steps of constructions: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 are 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 = 90° is made.

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

Step 6: OX is joined and and ∠XOY = 135° is constructed.

Thus, ∠XOY is the required angle making 135° with DY.