Question

What is the value of p?

180

58

116

90

Answer 1

Opposite angles in a cyclic quadrilateral add up to 180 degrees so

p = 180 - 90 = 90 degrees (answer).

Answer 2

Answer: The correct option is (D) 90.

Step-by-step explanation: We are given to find the value of p from the figure shown.

We note from the figure that

a quadrilateral is inscribed in a circle, so it is a cyclic quadrilateral.

Also, we know that the the sum of the opposite angles of a cyclic quadrilateral is 180°.

In the given circle, the opposite angle to the angle with measure p° is 90°.

Therefore, we must have

`p^\circ+90^\cir=180^\circ\\\\\Rightarrow p+90=180\\\\\Rightarrow p=180-90\\\\\Rightarrow p=90.`

Thus, the required value of p is 90.

Option (D) is CORRECT.