LAOB LAO & LEOQ Fou form linear pair FOC – 98 and cool = cro4= = 30 LCOB o ML DOE Find m

Question

LAOB
LAO & LEOQ Fou form linear pair
FOC
– 98 and cool = cro4=
= 30
LCOB
o
ML DOE
Find mL FOE, ML COB

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Eva 2 weeks 2021-11-15T08:25:05+00:00 1 Answer 0 views 0

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    2021-11-15T08:27:01+00:00

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    maahira17

    maahira17

    01.05.2020

    Math

    Secondary School

    +10 pts

    Answered

    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.

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    nikitasingh79

    nikitasingh79 Genius

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    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…..

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