Geometry : a trapezoid has angles that measures 3x°,3x°,x° and x°, what is the value of x?

Step-by-step explanation:

Any 4 sided figure closed and convex, has interior angles that add to 360 degrees

x + x + 3x + 3x = 360   Combine all like terms on the left.

8x = 360                       Divide both sides by 8

8x/8 = 360/8

x = 45

The value of x is 45.

9514 1404 393

  x = 100°

  y = 95°

Step-by-step explanation:

It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...

  y = 180° -85° = 95°

The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...

  90° +x = 2y

  x = 190° -90° = 100°

Additional comment

The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...

  2y +2(85°) = 360°

  y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary