QUIZ ON TYPES OF ANGLES

State whether the following are true (T) or false (F) :

Problem 1 :

An angle measuring 89^º is an acute angle.

Solution :

This statement is true.

Because, 89^º is less than 90^º.

Problem 2 :

An angle measuring 91^º is an obtuse angle.

Solution :

This statement is true.

Because, 91^º is less than 180^º.

Problem 3 :

The size of an angle depends on the lengths of its arms.

Solution :

The size of an angle depends upon the opening between its arms.

The size of an angle does not depend on the lengths of its arms.

So, this statement is false.

Problem 4 :

When a vertical line crosses a horizontal line the angle formed is a straight angle.

Solution :

A vertical line crosses a horizontal line the angle formed is a right angle.

So, this statement is false.

Problem 5 :

3/4 of a straight angle is an acute angle.

Solution :

This statement is false.

Because straight angle is180^º.

= 3/4 of 180

= (3/4) (180)

= 135 > 90

Then, 3/4 of a straight angle is an obtuse angle.

Problem 6 :

A right angle is neither an acute angle nor an obtuse angle.

Solution :

Right angle :

An angle that is exactly 90^º.

Acute angle :

An angle that is less than 90^º.

Obtuse angle :

An angle that is greater than 90^º and less than 180^º.

So, this statement is true.

State whether the following statements are true or false:

Problem 1 :

The sum of the angles of a triangle is equal to two right angles.

Solution :

The sum of the angles of a triangle = 180^º.

Right angle = 90^º.

The sum of the angles of a triangle = two right angles

180^º = 2 × 90^º

180^º = 180^º

So, this statement is true.

Problem 2 :

A right angled triangle can contain an obtuse angle.

Solution :

Right angle :

An angle that is exactly 90^º.

Obtuse angle :

An angle that is greater than 90^º and less than 180^º.

This statement is false.

So, a right angled triangle cannot contain an obtuse angle.

Problem 3 :

The sum of two angles of a triangle is always greater than the third angle.

Solution :

This statement is false.

Because, the sum of any two angles of a triangle is not always greater than the third angle.

Problem 4 :

The two smaller angles of a right angled triangle are supplementary.

Solution :

This statement is false.

Because, the two smaller angles of a right angled triangle are equal.

Problem 5 :

[XY] is a fixed line segment and [OP] can rotate about O between [OX] and [OY].

a. If a = 135, find b. b. If b = 67, find a. c. What is a if b is 27?

d. If a is 0, what is b? e. If a = 89, find b.

f. If a = b, what is the value of each?

Solution :

Given, [XY] is a fixed line segment.

a.  Given, a = 135

To find b:

[OX] + [OY] = [XY]

a + b = 180

135 + b = 180

b = 180 – 135

b = 45

b.  Given, b = 67

To find a:

[OX] + [OY] = [XY]

a + b = 180

a + 67 = 180

a = 180 – 67

a = 113

c.  Given, b = 27

To find a:

[OX] + [OY] = [XY]

a + b = 180

a + 27 = 180

a = 180 – 27

a = 153

d.  Given, a = 0

To find b:

[OX] + [OY] = [XY]

a + b = 180

0 + b = 180

b = 180 – 0

b = 180

e.  Given, a = 89

To find b:

[OX] + [OY] = [XY]

a + b = 180

89 + b = 180

b = 180 – 89

b = 91

f.  Given, a = b

[OX] + [OY] = [XY]

a + b = 180

b + b = 180

2b = 180

b = 180/2

b = 90

Problem 6 :

Tell whether the statement is always, sometimes, or never true. Explain.

a) If x and y are supplementary angles, then x is obtuse.

b)If x and y are right angles, then x and y are supplementary angles.

c) If x and y are complementary angles, then y is a right angle.

Solution :

a) When sum of angles is 180 degree, those angles are called supplementary to each other. Let those angles be x and y. One of the angle must be greater than 90 degree and the other angle may be less than 90 degree. Then, it is true. When two angles are the same and it is 90 degree, for that also as a sum we get 180 degree.

So, the given statement will be true sometimes.

b) When x and y are right angles, then x and y are supplementary angles. So, the given statement is always true.

c) The two angles are said to be complementary when the sum of the angles is 90 degree. Then one of the angle may not be 90 degree. Then it is never true.

Problem 7 :

Tell whether the angles are complementary, supplementary, or neither.

i)

ii)

Solution :

i) The sum of the angles shown

= 122 + 68

= 190

Since the sum of the angles is not 180, then it is not supplementary and it is neither.

ii) The sum of the angles = 42 + 48

= 90

Since the sum of the angles is 90, then they are complementary.