Geometry and Mensuration: Level 1 Test 5

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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:

$ \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 = 20^o
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
ThusAD²=CD²+AC²
By converse of Pythagoras theorem we can conclude that,
ACD =90^o.

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.