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Geometry and Mensuration: Level 1 Test 5

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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: 
72
$ \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: 
73
We know from Pythagoras theorem that
AB2 + BC2 = AC2
AD2 = AB2 + BC2 + CD2
ThusAD2 =CD2+AC2
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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