Question

1. quadrilateral abcd is inscribed in a circle. if angle a measures (3x - 10)° and angle c measures (2x)°, find x.

Explanation:

Step1: Recall cyclic quadrilateral property

In a cyclic quadrilateral, opposite angles are supplementary, so \( \angle A + \angle C = 180^\circ \).

Step2: Substitute angle measures

Given \( \angle A=(3x - 10)^\circ \) and \( \angle C=(2x)^\circ \), substitute into the equation:
\( (3x - 10)+2x = 180 \).

Step3: Solve for \( x \)

Combine like terms: \( 5x - 10 = 180 \).
Add 10 to both sides: \( 5x = 190 \).
Divide by 5: \( x=\frac{190}{5}=38 \).

Answer:

\( x = 38 \)