The angles of a quadrilateral are 4x, 7x, 15x and 10x. Find the smallest and the largestangles of the quadrilateral

To find the smallest and largest angles of the quadrilateral, we need to determine the values of x.

Step 1: Set up an equation using the sum of angles in a quadrilateral, which is 360 degrees.

4x + 7x + 15x + 10x = 360

Step 2: Combine like terms on the left side of the equation.

36x = 360

Step 3: Divide both sides of the equation by 36 to solve for x.

x = 10

Step 4: Substitute the value of x back into the expressions for the angles to find their values.

Smallest angle: 4x = 4(10) = 40 degrees Largest angle: 15x = 15(10) = 150 degrees

Therefore, the smallest angle of the quadrilateral is 40 degrees and the largest angle is 150 degrees.