The angles of a quadrilateral PQRS are 28°,(3x + 10), (4x +15) and (x - 5)". Find measure of each angle of the quadrilateral
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Answer:
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Step-by-step explanation:
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Correct option is
C
The measures of the angles are 38
0
,74
0
,76
0
and 172
0
Given, x,(3x−40),2x,(4x+20).
We know, by angle sum property, the sum of the angles of a quadrilateral is 360
0
.
Therefore, x+(3x−40)+2x+(4x+20)=360
o
⇒10x−20
o
=360
o
⇒10x=360
o
+20
o
=380
o
⇒x=
10
380
o
=38
o
.
Now, x=38
o
,
2x=2×38
o
=76
o
,
3x−40
o
=3×38
o
−40
o
=74
o
and 4x+20
o
=4×38
o
+20
o
=172
o
.
Thus, the measures of the angles are 38
o
,74
o
,76
o
and 172
o
.
Hence, option C is correct.
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