18. State the type of each of the following angles given below:
(i) 76°
(ii) 179°
(iii) 89.5°
(iv) 278°

19. Given figures are denoted as:
(i) A <-> B
(ii) P -> Q
(iii) x --- y

20. (i) One-fourth of a straight angle is ____
(ii) Two-third of a right angle is ____

21. Find the missing angle.

P
/\
30° | \
/ | \
Q----?----R
\ | /
50°

22. Name the sides and angles in the following figure.

X----Y
| |
W----Z

Let's identify the type of angles:

(i) 76° - This is an acute angle because it is less than 90°.
(ii) 179° - This is an obtuse angle because it is more than 90° and less than 180°.
(iii) 89.5° - This is also an acute angle as it is less than 90°.
(iv) 278° - This is a reflex angle because it is more than 180°.

Understanding the given figures:

(i) A <-> B - This notation typically represents a bidirectional or equivalence relation .
(ii) P -> Q - This denotes an implication or logical statement meaning if P, then Q.
(iii) x --- y - This notation might represent a line segment joining x and y .

Calculating angle fractions:

(i) One-fourth of a straight angle is 4 1 ​ × 18 0 ∘ = 4 5 ∘ , which is an acute angle.
(ii) Two-thirds of a right angle is 3 2 ​ × 9 0 ∘ = 6 0 ∘ , also an acute angle.

Finding the missing angle in triangle PQR:

In any triangle, the sum of angles is 180°. Given angles are 30° and 50°. Let the missing angle be x .
3 0 ∘ + 5 0 ∘ + x = 18 0 ∘
x = 18 0 ∘ − 8 0 ∘ = 10 0 ∘
So, the missing angle is 100°.

Naming sides and angles of the quadrilateral XYWZ:


Sides: XY, YZ, ZW, WX
Angles: ∠ XYW, ∠ YWZ, ∠ WZX, ∠ ZXY

Answered by AvaCharlotteMiller | 2025-07-06