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## Geometry and Mensuration: Test 26

Congratulations - you have completed Geometry and Mensuration: Test 26. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
 Question 1
The number of sides in two regular polygons are in the ratio 5: 4 and the difference between each interior angle of the polygons is 3o. Then the number of sides is
 A 15, 12 B 30, 24 C 10, 8 D 21, 16
Question 1 Explanation:
$\displaystyle \begin{array}{l}Let\text{ }the\text{ }number\text{ }of\text{ }sides\text{ }be\text{ }5xand\text{ }4xrespectively\\\frac{\left( 2\times 5x-4 \right){{90}^{o}}}{5x}-\frac{\left( 2\times 4x-4 \right)\times {{90}^{o}}}{4x}={{3}^{{}}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ \begin{array}{l}each\,\,\,\,\operatorname{int}erior\,\,angle\,\\=\left( \frac{2n-4}{n} \right)\times {{90}^{o}}\end{array} \right]\\\Rightarrow \left( 10x-4 \right)\times {{360}^{o}}-\left( 8x-4 \right)\times {{450}^{o}}=20x\times {{3}^{o}}\\\Rightarrow 120x-48-120x+60=2x\\\Rightarrow 2x=12\Rightarrow x=6\\Therefore\,\,\,Number\,\,of\,\,\,sides\\=30\,\,and\,\,24\end{array}$
 Question 2
ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. If ∠ABC= 72o, then the measure of the BCD is
 A 162o B 18o C 108o D 72o
Question 2 Explanation: Since ABCD is a cyclic trapezium, so its non parallel sides will be equal. Also AD || BC, so ∠ABC= ∠BCD => ∠BCD=72o Correct option is (d)
 Question 3
If an exterior angle of a cyclic quadrilateral be 50o, then the interior opposite angle is:
 A 130o B 40o C 50o D 90o
Question 3 Explanation:
The immediate internal angle = 1800-500 = 1300
The opposite internal angle = 1800 - 1300 = 500.
Correct option is (c).
 Question 4
The ratio of the length of the parallel sides of a trapezium is 3: 2. The shortest distance between them is 15cm. If the area of the trapezium is 450 cm2, the sum of the lengths of the parallel sides is
 A 15 cm B 36 cm C 42 cm D 60 cm
Question 4 Explanation:
$\begin{array}{l}\frac{1}{2}\times 15\times (\text{Sum of the length of two parallel sides})=450\\\text{Sum of length of parallel sides = 60}\text{.}\end{array}$
 Question 5
If the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is
 A 9√3cm B 6√3cm C 3√3cm D 6 cm
Question 5 Explanation:
$\begin{array}{l}Let\text{ }the\text{ }side\text{ }of\text{ }equilateral\text{ }triangle\text{ }be\text{ }x.\\\frac{1}{3}.\frac{\sqrt{3}}{2}x=3\\=>x=6\sqrt{3}\end{array}$
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