In Fig. 8.44, ∠AOF and ∠FOG form a linear pair.
∠EOB = ∠FOC = 90° and ∠DOC = ∠FOG = ∠AOB = 30°
(i) Find the measures of ∠FOE, ∠COB and ∠DOE.
(ii) Name all the right angles.
(iii) Name three pairs of adjacent complementary angles.
(iv) Name three pairs of adjacent supplementary angles.
(v) Name three pairs of adjacent angles.
Answers
Given : ∠AOF and ∠FOG form a linear pair.
∠EOB = ∠FOC = 90° and ∠DOC = ∠FOG = ∠AOB = 30°
Proof:
(i) Let ∠FOE = x , ∠DOE = y and ∠COB = z
∠AOF + ∠FOG = 180° (Linear pair)
∠AOF + 30° = 180°
∠AOF = 180° - 30°
∠AOF = 150°
But
∠AOF = ∠AOB + ∠BOC + ∠DOC + ∠DOE + ∠EOF
150° = 30° + z + 30° + y + x
150° = 60° + z + + y + x
150° - 60° = x + y + z
x + y + z = 90° …………..(1)
Now,
∠FOC = ∠FOE + ∠DOE + ∠DOC
90° = ∠FOE + ∠EOD + ∠DOC
90° = x + y + 30°
90° - 30° = x + y
x + y = 60° ……………. (2)
Put this value of x + y in eq 1, we obtain
x + y + z = 90°
60° + z = 90°
z = 90° - 60°
z = 30°
Then, ∠COB = 30°
Now,
∠EOB = ∠BOC + ∠COD + ∠DOE
90° = 30° + 30° + ∠DOE
90° = 60° + ∠DOE
∠DOE = 90° - 60°
∠DOE = 30°
But,
∠FOC = ∠FOE + ∠DOE + ∠DOC
90° = ∠FOE + ∠DOE + ∠DOC
90° = x + 30° + 30°
[∠DOE = 30°]
90° = x + 60°
x = 90° - 60°
x = 30°
∠FOE = x = 30°
Hence, the measures of ∠FOE, ∠COB and ∠DOE is 30°.
(ii) Right angles are:
∠AOD , ∠DOG, ∠FOC, ∠BOE
(iii) Three pairs of adjacent complementary angles are:
- ∠AOB, ∠BOD
- ∠AOC, ∠COD
- ∠BOC, ∠COE
(iv) Three pairs of adjacent supplementary angles are:
- ∠AOB, ∠BOG
- ∠AOC, ∠COG
- ∠AOD, ∠DOG
(v) Three pairs of adjacent angles are:
- ∠BOC, ∠COD
- ∠COD, ∠DOE
- ∠DOE, ∠EOF
HOPE THIS ANSWER WILL HELP YOU…..
Some questions of this chapter :
In Fig. 8.33, find x. Further find ∠BOC, ∠COD and ∠AOD.
https://brainly.in/question/15905575
In Fig. 8.40, ∠ACB is a line such that ∠DCA = 5x and ∠DCB = 4x. Find the value of x.
https://brainly.in/question/15905574
Answer:
all angle FOE, COB, DOE =30 degree
Step-by-step explanation:
I send u the pic of your answer please check the answer from that
