Question

find measure of all the marked angle in the following figure
​

Answer 1

Answer:

(b) x=30°; 4x=120°; 2x=60°

(c) a=15°; 3a=45°; 4a=60°;5a=75°

Answer 2

Answer:

IN FIGURE (b)

Since, XY is a line so, angle 4x and 2x form a linear pair

therefore,

➡ 4 x + 2 x = 180°

➡ 6 x = 180°

➡ x = 30°

So, two angle are-

• 4x = 4 (30°) = 120°
• 2x = 2 (30°) = 60°

Now, IN FIGURE (c)

Let, line CD and EF intersect at O

then,

angle EOC = angle DOF = 5a

Further,

Since, AB is a line

therefore,

➡ angle BOE + angle EOC + angle AOC = 180°

➡ 3a + 5a + 4a = 180°

➡ 12a = 180°

➡ a = 15°

Hence,

angles would be-

• 3a = 3 (15°) = 45°
• 5a = 5 (15°) = 75°
• 4a = 4 (15°) = 60°