Olympiad Test: Geometrical Shapes And Angles - 1

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.