Olympiad Test: Geometrical Shapes And Angles - 2

# Olympiad Test: Geometrical Shapes And Angles - 2

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## 20 Questions MCQ Test Math Olympiad for Class 5 | Olympiad Test: Geometrical Shapes And Angles - 2

Olympiad Test: Geometrical Shapes And Angles - 2 for Class 5 2023 is part of Math Olympiad for Class 5 preparation. The Olympiad Test: Geometrical Shapes And Angles - 2 questions and answers have been prepared according to the Class 5 exam syllabus.The Olympiad Test: Geometrical Shapes And Angles - 2 MCQs are made for Class 5 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Geometrical Shapes And Angles - 2 below.
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Olympiad Test: Geometrical Shapes And Angles - 2 - Question 1

### Which one of the following angles is not acute?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 1

An acute angle is less than 90°. 91° is more than 90°, so it is not acute.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 2

### Which one of the following angles is acute?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 2

An acute angle is less than 90° i.e. it is less than a right angle. Half a right angle (45°) is less than a right angle, so it is acute.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 3

### How many acute angles are there in the diagram?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 3

The following angles are all less than 90°, so are acute:
∠AOB, ∠BOC,∠COD,  ∠DOE, ∠AOC,
∠AOD, ∠BOD, ∠BOE and ∠COE
Therefore there are 9 acute angles altogether. Note that ∠AOE is obtuse.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 4

How many acute angles are there in this pentagram?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 4

Each of the five triangles at the points of the pentagram has three acute angles.
So there are 5 × 3 = 15 acute angles altogether in the pentagram. (All other angles are not acute)

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 5

How many acute angles are there in the diagram?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 5

The marked angles are all less than 90°, so are acute:

Therefore there are 10 acute angles altogether.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 6

How many acute angles are there in the diagram?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 6

The angles marked with arcs are all less than 90°, so are acute. The four angles around the top point are all right angles.
So there are 10 acute angles altogether.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 7

How many right angles are there in the diagram?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 7

Because one pair of lines is parallel (that is what the two arrows mean) and the other two lines are perpendicular to them (the little boxes mean right angles), the shape inside the four lines must be a rectangle. And there are 4 right angles at each of the four points where lines intersect. So there are 4 × 4 = 16 right angles altogether.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 8

How many right angles make two full rotations?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 8

A full rotation consists of four right angles. So two full rotations consist of eight right angles.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 9

Which one of the following angles is not obtuse?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 9

An obtuse angle is more than 90° but less than 180°.182° is more than 180°, so it is not obtuse.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 10

How many obtuse angles are there in the diagram?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 10

The following angles are obtuse:
∠AOD, ∠AOE, ∠AOF, ∠BOD, ∠BOE,
∠BOF, ∠COE and ∠COF.
Therefore, there are 8 obtuse angles altogether.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 11

Which one of the following angles is obtuse?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 11

Half a right angle = 45°
One right angle = 90°
One and a half right angles = 1½ × 90° = 135°
Two right angles = 180°
Only 135° is greater than 90° but less than 180°, so it is the only obtuse angle.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 12

How many straight angles are there in three full rotations?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 12

A full rotation consists of two straight (180°) angles.
So three full rotations consist of six straight angles.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 13

Which one of the following angles is not reflex?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 13

A reflex angle is more than 180° but less than 360°. 178° is less than 180°,
so it is not reflex. (All the rest are reflex angles.)

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 14

Which one of the following angles is reflex?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 14

A Reflex Angle is greater than 180° but less than 360°.
A, B and D are all less than 180°.
Only C is greater than 180° but less than 360°.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 15

If angle AOB = 67°, what is the size of reflex angle AOB?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 15

If you add the smaller angle (acute or obtuse) and the reflex angle for the same shape you will always come to 360°.
Therefore, reflex angle AOB = 360° − 67° = 293°

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 16

What is the least number of 33° angles you would need to make a reflex angle?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 16

2 × 33° = 66°, which is between 0° and 90°, so acute.
5 × 33° = 165°, which is between 90° and 180°, so obtuse.
6 × 33° = 198°, which is between 180° and 360°, so reflex.
7 × 33° = 231°, which is also reflex, but we have already found the least amount which is 6.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 17

Which of the following describes the triangle shown above?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 17

The triangle has three different lengths of side, so is scalene.
The triangle has lengths 3, 4 and 5 and 52 = 32 + 42 , so is right angled.
Therefore, it is a scalene right angled triangle.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 18

A triangle is isosceles and right angled. Which of the following statements must be false?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 18

Since the triangle is isosceles, it must have two equal angles. Since it is also right angled, the other two angles must both be 45° (45° + 45° +90° = 180°) So A is true.
Since the triangle is isosceles, it must have two of its sides equal. So B is true.
An isosceles triangle has one line of symmetry. So C is also true.
A triangle that satisfies A, B and C is shown in the following diagram:

Line l is the axis of symmetry Statement D must be false since a triangle with three different sides cannot be isosceles.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 19

Shraddha made two copies of the right angled triangle shown and cut them out.​She then joined edges of the triangles together to make shapes.  Which of the following shapes was it not possible for Shraddha to make?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 19

Shraddha could make an isosceles triangle, a parallelogram, a rectangle or a kite:

But the rectangle is not a square because the sides have different lengths.

Olympiad Test: Geometrical Shapes And Angles - 2 - Question 20

Shraddha made two copies of the following isosceles right angled triangle and cut them out. She then joined edges of the triangles together to make shapes.Which of the following shapes was it NOT possible for Shraddha to make?

Detailed Solution for Olympiad Test: Geometrical Shapes And Angles - 2 - Question 20

Shraddha could make a square, an isosceles triangle (one with 2 equal sides, 2 equal angles), and a parallelogram:

But she could not make an equilateral triangle (one with all equal sides, all equal angles).

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