x_{2}; 3(x - 10) . 3 = The angles of a quadrilateral add up to 360 degrees . Three of the angles , in degrees are 2x and a Write down an inequality for b Solve the inequality c Could the angles that are 2x degrees and Give a reason for your answer . 3(x - 10) degrees be the same size ?
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Answer:
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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