Quadrilateral CDEF is inscribed in circle A.

Question

Quadrilateral CDEF is inscribed in circle A.

If m∠FCD = (2x + 5)° and m∠FED = (3x − 10)°, what is the value of x?

19
35
37
73

Answer 1

Since quadrilateral CDEF is inscribed in circle A, the opposite angles are supplementary. This means that:

\[ m\angle FCD + m\angle FED = 180^\circ \]

Substituting the expressions for the angles, we get:

\[ (2x + 5) + (3x - 10) = 180 \]

Now, combine like terms:

\[ 2x + 5 + 3x - 10 = 180 \]

This simplifies to:

\[ 5x - 5 = 180 \]

Next, add 5 to both sides:

\[ 5x = 185 \]

Now, divide by 5:

\[ x = 37 \]

Thus, the value of \( x \) is \(\boxed{37}\).