Question

three angles of a parallelogram have the following measures: 58°, 122°, and 58°. what is the measure of the fourth angle? ∠4 = °

Explanation:

Step1: Recall the sum of interior angles of a parallelogram

The sum of the interior angles of a quadrilateral (a parallelogram is a type of quadrilateral) is \(360^{\circ}\).

Step2: Set up the equation

Let the fourth angle be \(x\). We know that \(58^{\circ}+122^{\circ}+58^{\circ}+x = 360^{\circ}\).
First, add the known angles: \(58 + 122+58=238\). So the equation becomes \(238^{\circ}+x = 360^{\circ}\).

Step3: Solve for \(x\)

Subtract \(238^{\circ}\) from both sides of the equation: \(x=360^{\circ}- 238^{\circ}\).
\(x = 122^{\circ}\)

Answer:

\(122\)