Question

I would really appreciate anyone who can answer this attached question, thanks.

Answer 1

The opposite angles of a cyclic quadrilateral are supplementary.

A + C = 180 degrees

3x - 10 + 2x = 180

5x = 190

x = 38

Answer: 38

We know A and C add to 180 because each is half the arc subtended, A=(1/2) arc BCD and C=(1/2) arc BAD. The two arcs together are the entire circle so,

A + C = (1/2) arc BCD + (1/2) arc BAD

= (1/2)(arc BCD + arc BAD) = (1/2)(360) = 180 degrees

Answer 2

In an inscribed quadrilateral, opposite angles add up to 180°.

So ∠A + ∠C = 180°.

(3x - 10) + 2x = 180

5x - 10 = 180

5x = 190

x = 38