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## Geometry and Mensuration: Level 1 Test 5

Congratulations - you have completed Geometry and Mensuration: Level 1 Test 5. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
 Question 1
An angle is equal to 1/3 of its supplement. Find its measure.
 A 60 degrees B 80 degrees C 90 degrees D 45 degrees
Question 1 Explanation:
$\displaystyle \begin{array}{l}\operatorname{Re}quired\,\,angle\,\,x=\frac{1}{3}\left( 180-x \right)\\4x=180\\x={{45}^{0}}\end{array}$
 Question 2
In ΔABC, ∠BAC= 90 degrees and AB= 1/2BC. Then the measure of ∠ACB is:
 A 60 degrees B 30 degrees C 45 degrees D 15 degrees
Question 2 Explanation:

\$ \displaystyle \begin{array}{l}~Since\text{ }AB\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }BC,\\ACB\text{ }
 Question 3
How many sides a regular polygon has with its interior angle eight times its exterior angle?
 A 16 B 24 C 18 D 20
Question 3 Explanation:
Let the interior angle be x,
Thus, x= 8(180-x)
=> 9x= 8(180) => x = 160
The exterior angle = 20o
The number of sides=360/20 = 18
 Question 4
In a quadrilateral ABCD, ∠B= 90 degrees and AD2 = AB2 + BC2 + CD2, then ∠ACD is equal to
 A 90 degrees B 60 degrees C 30 degrees D None of these
Question 4 Explanation:

We know from Pythagoras theorem that
AB2 + BC2 = AC2
AD2 = AB2 + BC2 + CD2
By converse of Pythagoras theorem we can conclude that,
ACD =90o.
 Question 5
If the lengths of the three sides of a triangle are 6 cm, 8 cm and 10 cm, then the length of the median to its greatest side is.
 A 8 cm B 6 cm C 5 cm D 4.8 cm
Question 5 Explanation:
Now since BD = median AD= BC.
Now since 82+62=102
The  triangle is a right angled triangle (right angle at B)
Thus BD = AD=BC=1/2 x 10 =5 cm
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