Question

Quadrilateral ABCD is inscribed in a circle. Angle B measures (x – 5)°, and angle D measures (3x + 5)°. Find x.

Answer 1

Angle B is opposite to angle D.
Since quadrilateral ABCD is inscribed in a circle, it’s a cyclic quadrilateral.
The sum of the opposite angles of a cyclic quadrilateral is 180 degrees.
(x-5)+(3x+5)=180
4x=180
x=180/4
x=65 degrees

Answer 2

Answer: x = 45

Step-by-step explanation:

Quadrilaterals inscribed in a circle have all four vertices on the circle.

A unique property of these types of quadrilaterals is their angle measures: Opposite angles of inscribed quadrilaterals will always add up to 180 (they are supplementary angles).

As such, the inscribed quadrilateral ABCD has opposite angles at AC and BD. Because the quadrilateral is inscribed, this means that the angles A + C and the angles B + D will equal 180 degrees. We can represent the angles measures for B and D in an equation where B + D = 180:

$(x-5)+(3x+5)=180\\\\4x = 180\\\\x=45$

When x = 45, the angle B is 40 degrees and the angle D is 140 degrees.