Question

What is the value of d?

Answer 1

Since the sum of the opposite angles of a cyclic quadrilateral are supplementary, the value of d is equal to 80°.

In Mathematics, the measure of the sum of two (2) adjacent angles would be equal to 180º when a quadrilateral is inscribed in a circle. Generally speaking, any cyclic quadrilateral would have all of its vertices on the circumference of a circle.

This ultimately implies that, the sum of the opposite angles of a quadrilateral that is inscribed in a circle (cyclic quadrilateral) are supplementary;

m∠c + 96 = 180°

m∠d + 100 = 180°

Now, we can solve for the value of d by by subtracting 100 from both sides of the equation as follows;

m∠d + 100 - 100 = 180° - 100

m∠d = 80°

Answer 2

The measure of angle d is
`80\°`

Explanation:

we know that

In an inscribed quadrilateral, the opposite angles are supplementary

so

`m>d+100\°=180\°`

`m>d=180\°-100\°=80\°`