Question
Quadrilateral CDEF is inscribed in circle A.
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
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
Answers
GPT-4o mini
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 \(\boxed{37}\).
\[
m\angle FCD + m\angle FED = 180^\circ
\]
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 \(\boxed{37}\).