The measure of the angle of a quadrilateral are in the ratio 2:3:7:6 find their measure in degree and radians. State with reasons whetherthe quadrilateral is cyclic.
Answers
Answer:
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Given:
The angles of a quadrilateral are in the ratio 2:3:7:6.
To Find:
the measure of degree and radians
to state whether it is a cyclic quadrilateral.
Solution:
Let the angles of the quadrilateral be 2x, 3x, 7x, 6x
Angle sum property of the quadrilateral = 360°
2x+3x+7x+6x = 360°
18x = 360°
x = 20
So, the angles of the quadrilateral after putting the value of x is
2x = 2×20=40°
3x = 3×20=60°
7x = 7×20=140°
6x = 6×20=120°
So, if the sum of the opposite interior angles is 180° then it is a cyclic quadrilateral.
The sum of the opposite interior angle are = 140° + 40°
= 180°
Therefore, it is a cyclic quadrilateral.