Question

4 po
6) The sum of 3 angles of a
quadrilateral is 5 times the fourth.
The fourth angle is​

Answer 1

Let ,

the fourth angel be 'x'

Therefore, sum of 3 angles = 5x

we know,

sum of all angles of a quadrilateral is 360°.

5x + x = 360

6x = 360

x = 60°

Answer :

The fourth angle measures 60°

Answer 2

Answer:

let the sum of three angles be X

& let the fourth angle be y

then the fourth angle, y

=According to the question

the sum of three angles (X) of the quad... is equal to 5 times the fourth angle(y)

OR

y×5=X

-----y=X/5----

Now we know that the sum of 4 angles of a quad.. is 360.

OR

[angle1 + angle2 + angle3 + angle4]= 360

OR

[{{angle1 + angle2 + angle3}} + angle4]= 360

[X + y] = 360[angle1 + angle2 + angle3 = X]

[ angle4 =y].

[X + X/5]= 360 [value of y is X/5]

(5X + X)/5=360 (((((we take LCM of 5&1=5. So we multiplied X by 5and it became 5X)))))

6X/5=360

6X=360×5 {{we transposed 5 from LHS to RHS due to which its relation changed from ÷ to ×}}

X=1800/6{{we transposed 6 from LHS to RHS due to which its sign changes from × to ÷}}

X=300

Now the fourth angle = y = X/5 = 300/5=60

SO THE FOURTH ANGLE MEASURES 60°.

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