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

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:

[tex](x-5)+(3x+5)=180\\\\4x = 180\\\\x=45[/tex]

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

ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-08-13T10:10:20+02:00

The value of x is 45°.

It is required to find the value of x.

What is quadrilateral?

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. Quadrilaterals are also called quadrangles and tetragons.

Given that:

By the Concept of the Quadrilaterals.

Basically we know that, the sum of opposite angles of a quadrilateral inscribed in a circle is always 180°.

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.

so applying this law here, we get as,

(x – 5)°+(3x + 5)°=180°

4x=180°

x=180°/4

x=45°

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

So, the value of x is 45°.

Learn more about quadrilateral here:

https://brainly.com/question/16418395

#SPJ5