Question

ABCD is a quadrilateral inscribed in a circle, as shown below:

Answer 1

Answer:

• A. (x + 16) + (6x − 4) = 180

Step-by-step explanation:

Inscribed quadrilateral has opposite angles supplementary.

So

• m∠A + m∠C = 180°

or

• m∠B + m∠D = 180°.

Since

• m∠A = x + 16,
• m∠B = x,
• m∠C = 6x - 4,
• m∠D = 2x + 16

we can use either pair of angle measures to work out the value of x and then find the value of each angle.

We can verify the first option is the only correct one.

• m∠A + m∠C = 180°
• (x + 16) + (6x − 4) = 180