The values of x in the cyclic quadrilateral are 6.67 and 25 and the angle
m∠ ACB is 115°
Cyclic Quadrilateral
A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral. The circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle.
1)
Let's solve to find the value of x
Using proportions;
12/8 = 10 / x
x = 20 / 3
x = 6.67
2) To find x;
(4x + 15)° + (6x + 3)° + 92° = 360°
Sum of angles in a circle is 360°
4x + 15 + 6x + 3 + 92 = 360
10x + 110 = 360
10x = 250
x = 25
To find the value of m ∠ACB in the quadrilateral, we have to evaluate the value of x in the expression = 4x + 15
m∠ ACB = 4(25) + 15
m ∠ ACB = 115°
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