Question

problem 11: (first taught in lesson 30) find the measures of the angles of an isosceles right triangle. after you enter your answer press go. go

Explanation:

Step1: Recall the properties of a right - triangle

In a right - triangle, one angle is \(90^{\circ}\). Let the other two angles be \(x\) and \(y\). By the angle - sum property of a triangle, \(x + y+90^{\circ}=180^{\circ}\), so \(x + y=90^{\circ}\).

Step2: Use the property of an isosceles triangle

Since the triangle is isosceles, \(x = y\). Substitute \(y=x\) into \(x + y=90^{\circ}\). We get \(x+x = 90^{\circ}\), or \(2x=90^{\circ}\).

Step3: Solve for \(x\)

Divide both sides of the equation \(2x = 90^{\circ}\) by 2. So \(x=\frac{90^{\circ}}{2}=45^{\circ}\), and \(y = 45^{\circ}\).

Answer:

\(45^{\circ},45^{\circ},90^{\circ}\)