Question

Angle C is an inscribed angle of circle P. Angle C measures (x + 5)° and arc AB measures (4x)° . Find x.

Answer 1

Step-by-step explanation:

$m \angle \: C = \frac{1}{2} (m \: arc \: AB)\\(By\:inscribed \:\angle\:theorem) \\ \\ \therefore \: (x + 5) \degree =\frac{1}{2} (4x)\degree \\ \\ \therefore \: x + 5=\frac{1}{2} \times 4x \\ \\ \therefore \: x + 5=2x \\ \\ \therefore \: x - 2x = - 5 \\ \\ \therefore \: - x = - 5 \\ \\ \: \: \: \: \: \huge \purple{ \boxed{\therefore \: x = 5}}$