Question

In the diagram below, Pis circumscribed about quadrilateral ABCD. What is
the value of x?
A. 60°
B. 100°
C. 80°
D. 120°

Answer 1

Answer:

c

Step-by-step explanation:

x=180-100=80

Answer 2

The value of x is $80^{o}$.

What are the opposite angle of a quadrilateral?

The opposite angles in a quadrilateral are those angles that are located diagonally opposite to each other.

What is the sum of the opposite angles of a quadrilateral?

The sum of the opposite angles of a cyclic quadrilateral is 180 degrees.

According to the given question.

We have a quadrilateral ABCD which is inscribed in a circle.

Also, m ∠ABC = 100 degrees

Since, we know that the sum of the opposite angles of a cyclic quadrilateral is 180 degrees.

Therefore,

$m\angle ABC +m\angle CDA = 180^{o} \\\implies 100^{o} + x = 180^{o} \\\implies x = 180^{o} -100^{o} \\\implies x = 80^{o}$

Hence, the value of x is $80^{o}$.

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