Question

Consider Quadrilateral ABCD inscribed in circle E. If m A = 38x + 5°, and mC = 21x - 2. solve for x.

Answer 1

Answer:

x=3

Explanation:

Angles A and C are opposite angles of a cyclic quadrilateral.

Theorem:

Therefore:

$\begin{gathered} m\angle A+m\angle C=180\degree \\ 38x+5\degree+21x-2=180\degree \end{gathered}$

Next, solve the equation for x:

$\begin{gathered} 38x+21x+5-2=180 \\ 59x+3=180 \\ 59x=180-3 \\ 59x=177 \\ x=\frac{177}{59} \\ x=3 \end{gathered}$

The value of x is 3.