Test: Constructions- Case Based Type Questions

# Test: Constructions- Case Based Type Questions - Class 9

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Test: Constructions- Case Based Type Questions - Question 1

### An architect was asked to make a triangular portico with a base 7 m and the angle to its base should be tilted 75° and the sum of other two sides of the portico be 13 mQ. If the other base angle is 60°, what will be the measure of the third angle :

Detailed Solution for Test: Constructions- Case Based Type Questions - Question 1
Third angle = x

∴ 60° + 75° + x =180° (Angle sum property of triangle)

x = 180 – 135

x = 45°

Test: Constructions- Case Based Type Questions - Question 2

### An architect was asked to make a triangular portico with a base 7 m and the angle to its base should be tilted 75° and the sum of other two sides of the portico be 13 mQ. Will the architect the able to draw an angle of 75° with ruler and compass only :

Detailed Solution for Test: Constructions- Case Based Type Questions - Question 2
Yes, it is possible to draw an angle of 750 with ruler and compass only.

Step of Construction:

(i) Take a ray OA.

(ii) With O as centre and any convenient radius, draw an arc cutting OA at C.

(iii) With C as centre and the same radius, draw an cutting the first arc at M.

(iv) With M as centre and the same radius, cut off an arc cutting again the first arc at L.

(v) With L and M as centre and radius of more than half of LM, draw two arcs cutting each other at B, join OB which is making 90°.

(vi) Now with N and M as centres again draw two arcs cutting each other at P.

(vii) Join OP.

Then, ∠POA = 75°.

Test: Constructions- Case Based Type Questions - Question 3

### An architect was asked to make a triangular portico with a base 7 m and the angle to its base should be tilted 75° and the sum of other two sides of the portico be 13 mQ. What should be known by the architect to justify the construction :

Detailed Solution for Test: Constructions- Case Based Type Questions - Question 3
Properties and theorems should be known by the architect to justify the construction.
Test: Constructions- Case Based Type Questions - Question 4

An architect was asked to make a triangular portico with a base 7 m and the angle to its base should be tilted 75° and the sum of other two sides of the portico be 13 m

Q. What will be the measure of each angle of 75° angle is bisected once :

Detailed Solution for Test: Constructions- Case Based Type Questions - Question 4

Test: Constructions- Case Based Type Questions - Question 5

An architect was asked to make a triangular portico with a base 7 m and the angle to its base should be tilted 75° and the sum of other two sides of the portico be 13 m

Q. Which of the following sets of angles can be angle of triangle :

Detailed Solution for Test: Constructions- Case Based Type Questions - Question 5
The sum of all 3 angles of a Δ = 180°

∴ 50° + 30° + 100° = 180°

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