In figure, and from a linear pair. If = =90^ and = = =30^ . 1. Find the measure of , and . 2. Name all the right angles. 3. Name three pairs of adjacent complementary angles. 4. Name three pairs of adjacent supplementary angles. 5. Name three pairs of adjacent angles

1. =x, =y and =z Since , is a linear pair +30=180 =180-30 =150 + + + + =150 30 + z + 30 + y + x = 150 x + y + z =150 - 30 - 30 x + y + z = 90 ...(1) =90^ + + =90^ x + y + 30 = 90 x + y = 90 - 30 x + y = 60 ...(2) Substituting (2) in (1) x + y + z = 90 60 + z = 90 z = 90 - 60 = 30 Given BOE = 90 + + =90^ 30 + 30 + DOE = 90 DOE = 90 - 60 = 30 DOE = x = 30 We also know that, x + y = 60 y = 60 - x y = 60 - 30 y = 30 Thus we have =30, =30 and =30 2. Right angles are: , , , . 3. Adjacent complementary angles are: ( , );( , );( , ). 4. Adjacent supplementary angles are: ( , );( , );( , ). 5. Adjacent angles are: ( , );( , );( , ).

In figure, and from a linear pair. If = =90^ and = = =30^ . 1. Fi…

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Question

In figure, $\angle\text{AOF}$ and $\angle\text{FOG}$ from a linear pair. If $\angle\text{EOB}=\angle\text{FOC}=90^\circ$ and $\angle\text{DOC}=\angle\text{FOG}=\angle\text{AOB}=30^\circ.$

Find the measure of $\angle\text{FOE},\angle\text{COB}$ and $\angle\text{DOE}.$
Name all the right angles.
Name three pairs of adjacent complementary angles.
Name three pairs of adjacent supplementary angles.
Name three pairs of adjacent angles

✓

Answer

$\angle\text{FOE}=\text{x},\angle\text{DOE}=\text{y}$ and $\angle\text{BOC}=\text{z}$

Since $\angle\text{AOF},\angle\text{FOG}$ is a linear pair

$\angle\text{AOF}+30=180$

$\angle\text{AOF}=180-30$

$\angle\text{AOF}=150$

$\angle\text{AOB}+\angle\text{BOC}+\angle\text{COD}+\angle\text{DOE}+\angle\text{EOF}=150$

30 + z + 30 + y + x = 150

x + y + z =150 - 30 - 30

x + y + z = 90 ...(1)

$\angle\text{FOC}=90^\circ$

$\angle\text{FOE}+\angle\text{EOD}+\angle\text{DOC}=90^\circ$

x + y + 30 = 90

x + y = 90 - 30

x + y = 60 ...(2)

Substituting (2) in (1)

x + y + z = 90

60 + z = 90

z = 90 - 60 = 30

Given BOE = 90

$\angle\text{BOC}+\angle\text{COD}+\angle\text{DOE}=90^\circ$

30 + 30 + DOE = 90

DOE = 90 - 60 = 30

DOE = x = 30

We also know that,

x + y = 60

y = 60 - x

y = 60 - 30

y = 30

Thus we have $\angle\text{FOE}=30,\angle\text{COB}=30$ and $\angle\text{DOE}=30$

Right angles are:
$\angle\text{DOG},\angle\text{COF},\angle\text{BOF},\angle\text{AOD}.$
Adjacent complementary angles are:

$(\angle\text{AOB},\angle\text{BOD});(\angle\text{AOC},\angle\text{COD});(\angle\text{BOC},\angle\text{COE}).$