Question

a. 115° b. 120° c. 125° d. 145° e. 150°

1. the perimeter of a parallelogram is 76 inches, and 1 side measures 14 inches. if it can be determined, what are the lengths, in inches, of the other 3 sides? a. 14, 14, 34 b. 14, 17, 17 c. 14, 24, 24 d. 14, 31, 31 e. cannot be determined from the given information

Explanation:

Step1: Recall triangle - exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle ABC\), \(\angle ACD\) is an exterior angle, and \(\angle A\) and \(\angle B\) are the non - adjacent interior angles.

Step2: Calculate \(\angle ACD\)

We know that \(\angle A = 35^{\circ}\) and \(\angle B=115^{\circ}\). So, \(\angle ACD=\angle A+\angle B\).

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for parallelogram problem:

Step1: Use the formula for the perimeter of a parallelogram

The perimeter \(P\) of a parallelogram is given by \(P = 2(a + b)\), where \(a\) and \(b\) are the lengths of two adjacent sides. Let one side \(a = 14\) inches and \(P=76\) inches.

Step2: Substitute values into the perimeter formula

We have \(76=2(14 + b)\). First, divide both sides of the equation by 2: \(\frac{76}{2}=14 + b\), which simplifies to \(38=14 + b\).

Step3: Solve for \(b\)

Subtract 14 from both sides: \(b=38 - 14=24\) inches. In a parallelogram, opposite sides are equal. So the lengths of the other three sides are 14 inches, 24 inches, 24 inches.

Answer:

E. \(150^{\circ}\)