the angles of a quidrelateral are (5x) degree, 5(x+2) degree, (6x-20) degree and 6(x+3) degree respectively. find (i) the value of x and (ii) each angle of the quiedrilateral
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Angles of a quadrilateral are (4x)
∘
, 5(x+2)
∘
, (7x−20)
∘
and 6(x+3)
∘
.
(i) Find the value of x (in degrees).
(ii) Each angle of the quadrilateral
Medium
Solution
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The given angles of a quadrilateral are (4x0
o
.5(x+2)
o
,(7x−20)
o
and 6(x+3)
o
.
We know that in quadrilateral sum of the four angles is 360
o
.
∴ 4x+5(x+2)+7x−20+6(x+3)=360
o
⇒ 4x+5x+10
o
+7x−20
o
+6x+18
o
=360
o
.
⇒ 22x+8
o
=360
o
⇒ 22x=352
o
⇒ x=
22
352
o
∴ x=16
o
Now, we are going to find each angle of the quadrilateral.
⇒ (4x)
o
=4×16
o
=64
o
⇒ 5(x+2)
o
=5(16
o
+2
o
)=5(18
o
)=90
o
⇒ (7x−20)
o
=(7×16
o
−20)
o
=92
o
⇒ 6(x+3)
o
=6(16
o
+3
o
)=6(19
o
)=114
o
∴ Measure of the angles of quadrilateral are 64
o
,90
o
,92
o
and 114
o
.