Question

progress: the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. a trapezoid has interior angle measures of 95°, 97°, 85° and x degrees. find the measure of angle x in the trapezoid. enter only the number of degrees in the answer box. the solution is

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral.

The sum of the interior angles of any quadrilateral is \( 360^\circ \). For a trapezoid, which is a type of quadrilateral, this property holds.

Step2: Set up the equation to find \( X \).

We know three of the interior angles: \( 95^\circ \), \( 97^\circ \), and \( 85^\circ \), and the fourth angle is \( X \). So we can write the equation:

$$ 95 + 97 + 85 + X = 360 $$

Step3: Calculate the sum of the known angles.

First, add the known angles: \( 95 + 97 + 85 = 95 + 85 + 97 = 180 + 97 = 277 \).

Step4: Solve for \( X \).

Substitute the sum of the known angles into the equation:

$$ 277 + X = 360 $$

Subtract 277 from both sides to solve for \( X \):

$$ X = 360 - 277 = 83 $$

Answer:

83