Quadrilaterals Test

Result

Quadrilaterals Test - 1

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Question 1
1 / -0

The opposite angles of a quadrilateral are equal and the adjacent angles are in ratio 1 : 3. What will be the measure of all the angles in ascending order?

A
30°, 30°, 150° and 150°

B
25°, 25°, 155° and 155°

C
45°, 45°, 135°and 135°

D
40°, 40°, 140° and 140°

Solution

Let the angles be x, x, 3x and 3x.
According to angle sum property,

x + x + 3x + 3x = 360°
8x = 360°
x = 45°

So, the angles are 45°, 45°, 135° and 135°.
Question 2
1 / -0

If two consecutive angles of a parallelogram are (x + 80)° and (5x + 40)°, what is the name of the quadrilateral?

A
Rhombus

B
Rectangle

C
Trapezium

D
Parallelogram

Solution

We know that consecutive interior angles of a parallelogram are supplementary.

(x + 80)° + (5x + 40)° = 180°
6x° + 120° = 180°

6x° = 60°
x° = 10°

Thus, two consecutive angles are (10 + 80)° and (5 × 10 + 40)°, i.e. 90° and 90°. Hence, the name of the given parallelogram is rectangle.
Question 3
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In a quadrilateral ABCD, if ∠A = 90° and ∠B : ∠C : ∠D = 3 : 4 : 8, then what will be the measures of the other angles?

A
∠B = 54°, ∠C = 92° and ∠D = 124°

B
∠B = 54°, ∠C = 72° and ∠D = 144°

C
∠B = 74°, ∠C = 62° and ∠D = 134°

D
∠B = 84°, ∠C = 72° and ∠D = 144°

Solution

Let ∠B = 3x, ∠C = 4x and ∠D = 8x
Now, ∠A + ∠B + ∠C + ∠D = 360°

90° + 3x + 4x + 8x = 360°
15x = 270°

x = 18°
So, ∠B = 3 × 18, ∠C = 4 × 18 and ∠D = 8 × 18
∠B = 54°, ∠C = 72° and ∠D = 144°