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 theorem

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

Step2: Solve for equiangular triangle (part a)

Let each angle of the equiangular triangle be \(x\). Since there are 3 angles and their sum is 180°, we have the equation \(x + x+x=180^{\circ}\), or \(3x = 180^{\circ}\). Solving for \(x\), we get \(x=\frac{180^{\circ}}{3}=60^{\circ}\).

Step3: Solve for isosceles triangle (part b)

Let the measure of one of the non - right angles be \(y\). In an isosceles triangle, two angles are equal. If one angle is 90°, then \(y + y+90^{\circ}=180^{\circ}\) (by the triangle - angle sum theorem). Combining like terms gives \(2y=180^{\circ}- 90^{\circ}=90^{\circ}\). Solving for \(y\), we get \(y = 45^{\circ}\).

Answer:

a. Each angle measures 60°.
b. The other two angles each measure 45°.