Olympiad Test: Geometrical Shapes And Angles - 1 - Class 5 MCQ

Since 89° is less than 90°, it is acute.

Since 234° is greater than 180°, it is reflex.

Since 98° is greater than 90° but less than 180°, it is obtuse

Measuring from O (Alphabet) in the direction of the arrow, angle AOB = 57°

Starting from O, and measuring in the direction of the arrow, angle COD = 131°

Reflex Angle FOE can be split into two: Angle FOE = Angle FOG + Angle GOE
Angle FOG is a straight angle
∴ ∠FOG= 180°. Now, starting from O and measuring in the direction of the arrow
Angle GOE = 74°
So Reflex Angle FOE = Angle FOG + Angle GOE = 180° + 74° =254°

The vertex (plural vertices) is a corner point of two rays.

The middle letter is where the angle actually is (its vertex), which is D. Therefore we could write the angle as ∠BDA or ∠ADB.

The middle letter is where the angle actually is (its vertex), which is C. Therefore we could write the angle as ∠BCD or ∠DCB.

An acute angle is less than 90°.
If you add two acute angles then
(i) The sum could be acute, example: 10° + 20° = 30° (an acute angle).
(ii) The sum could be right, example: 40° + 50° = 90° (a right angle).
(iii) The sum could be obtuse, example: 30° + 80° = 110° (an obtuse angle).
(iv) the sum could NOT be straight because each acute angle is less than 90° and a straight angle is 180°, example: 89° + 89° = 178° which is less than a straight angle.

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

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.

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.

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)

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

Therefore, there are 10 acute angles altogether.

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.

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.

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

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

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