Question

a trapezoid has interior angle measures of 90°, 90°, 75° and x degrees. find the measure of angle x in the trapezoid. enter only the number of degrees in the answer box. angle x measures ______ degrees. the solution is

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\).

Step2: Set up the equation

We know three angles: \(90^{\circ}\), \(90^{\circ}\), \(75^{\circ}\) and the fourth angle \(X\). So, \(90 + 90+75+X = 360\).

Step3: Simplify the left - hand side of the equation

\(90+90 + 75+X=(90 + 90)+75+X=180+75+X=255+X\).

Step4: Solve for \(X\)

Subtract \(255\) from both sides of the equation \(255+X = 360\). We get \(X=360 - 255\).

Answer:

\(105\)