Question

Segments AB and BC are tangent to circle P.

What is the value of x? Show your work and explain your reasoning. (CER)

Answer 1

x = 82°

Explanation:

From inspection of the given diagram:

• Point P is the center of circle P.
• Line segments PA and PC are the radii of circle P
• Line segments AB and BC are tangent to circle P.

The tangent of a circle is always perpendicular to the radius.

Therefore, m∠BAP = m∠BCP = 90°.

Since the sum of the interior angles in a quadrilateral is 360°, then:

⇒ m∠BAP + m∠APC + m∠BCP + m∠ABC = 360°

⇒ 90° + 98° + 90° + x = 360°

⇒ 278° + x = 360°

⇒ 278° + x - 278° = 360° - 278°

⇒ x = 82°

Therefore, the value of x is 82°.