Question

In the diagram below, point P is circumscribed about quadrilateral ABCD. What is the value of x? (Pls answer I give lot of point)

Answer 1

D. 50

Explanation:

130+x=180

x=50

Answer 2

The value of
`\( x \)` is 50 degrees, which corresponds to option D.

The diagram shows a circle circumscribed around quadrilateral ABCD, with an angle at C that is 130 degrees. Assuming that ABCD is a cyclic quadrilateral (a quadrilateral whose vertices all lie on the circumference of a circle), then the opposite angles of a cyclic quadrilateral sum up to 180 degrees due to the Inscribed Angle Theorem. This theorem states that the opposite angles of a cyclic quadrilateral are supplementary.

Given that angle
`\( \angle C \)` is 130 degrees, we can find the measure of angle
`\( \angle A \)` by the following relationship for a cyclic quadrilateral:

`\[ \angle A + \angle C = 180^\circ \]`

Plugging in the value for
`\( \angle C \)`, we get:

`\[ \angle A + 130^\circ = 180^\circ \]`

Now, let's calculate the value of angle
`\( \angle A \)`:

`\[ \angle A = 180^\circ - 130^\circ \]`

`\[ \angle A = 50^\circ \]`

Therefore, The answer is 50 degrees.