Question

find angle x.
(1 point)

Explanation:

Step1: Find the adjacent angle of \(152^{\circ}\)

The sum of adjacent angles on a straight line is \(180^{\circ}\). Let the adjacent angle be \(y\), then \(y = 180^{\circ}- 152^{\circ}=28^{\circ}\)

Step2: Use the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral is \(360^{\circ}\). We know three angles: \(90^{\circ}\), \(y = 28^{\circ}\), and assume the fourth - angle is \(x\). So \(90^{\circ}+x + 28^{\circ}+180^{\circ}=360^{\circ}\) (the sum of angles around a point is \(360^{\circ}\), but here we can also use the property of the sum of interior angles of a polygon. For a four - sided figure with one angle formed by a straight - line split, we can write \(90^{\circ}+x+28^{\circ}+180^{\circ}=360^{\circ}\)). Simplifying gives \(x+298^{\circ}=360^{\circ}\)

Step3: Solve for \(x\)

Subtract \(298^{\circ}\) from both sides: \(x=360^{\circ}-298^{\circ}=62^{\circ}\)

Answer:

\(62^{\circ}\)