Question

Quadrilateral cdef is inscribed in circle a. if m∠def = (3x + 7)° and m∠dcf = (2x + 8)°, what is the value of x?

Option 1: 21
Option 2: 33
Option 3: 39
Option 4: 69

Answer 1

To find the value of x in the given quadrilateral, we can set up an equation using the given angles and solve for x.

Step-by-step explanation:

To find the value of x, we can set up an equation using the given angles in the quadrilateral.

m∠def = (3x + 7)° = m∠cfed (opposite angles in a cyclic quadrilateral)

m∠dcf = (2x + 8)° = m∠dec (opposite angles in a cyclic quadrilateral)

Since the sum of the angles in a quadrilateral is 360°, we can set up the equation:

m∠def + m∠dcf + m∠dec + m∠cdf = 360°

(3x + 7)° + (2x + 8)° + (3x + 7)° + (2x + 8)° = 360°

Simplifying the equation:

10x + 30 + 15 = 360

10x + 45 = 360

Subtracting 45 from both sides:

10x = 315

Dividing both sides by 10:

x = 31.5

The value of x is 31.5.