Question

1. look for relationships use the triangle angle - sum theorem to answer the following questions. explain your answers. a. what are the measures of each angle of an equiangular triangle? b. if one of the angle measures of an isosceles triangle is 90, what are the measures of the other two angles?

Explanation:

Step1: Recall triangle - angle - sum property

The sum of the interior angles of a triangle is 180°.

Step2: Solve for angles of equiangular triangle

For an equiangular triangle, let each angle be \(x\). Then \(x + x+x=180^{\circ}\), so \(3x = 180^{\circ}\), and \(x=\frac{180^{\circ}}{3}=60^{\circ}\).

Step3: Solve for angles of isosceles right - triangle

In an isosceles right - triangle, one angle is 90°. Let the other two equal angles be \(y\) each. Using the angle - sum property \(90^{\circ}+y + y=180^{\circ}\), which simplifies to \(90^{\circ}+2y=180^{\circ}\). Subtract 90° from both sides: \(2y=180^{\circ}-90^{\circ}=90^{\circ}\), then \(y = 45^{\circ}\).

Answer:

a. Each angle of an equiangular triangle measures 60°.
b. In an isosceles triangle with one angle 90°, the other two angles each measure 45°.