Question

problem 17: (first taught in lesson 30) find the measures of the angles of an isosceles triangle with a vertex angle of 42°. after you enter your answer press go. go

Explanation:

Step1: Recall the property of isosceles triangle

In an isosceles triangle, the base - angles are equal. Let the vertex angle be \(A = 42^{\circ}\), and the base - angles be \(B\) and \(C\). Also, by the angle - sum property of a triangle, \(A + B + C=180^{\circ}\).

Step2: Substitute the values into the angle - sum formula

Since \(B = C\), we have \(42^{\circ}+B + B=180^{\circ}\). This simplifies to \(42^{\circ}+2B = 180^{\circ}\).

Step3: Solve for \(B\)

Subtract \(42^{\circ}\) from both sides: \(2B=180^{\circ}- 42^{\circ}=138^{\circ}\). Then divide both sides by 2: \(B=\frac{138^{\circ}}{2}=69^{\circ}\), and \(C = B = 69^{\circ}\).

Answer:

\(42^{\circ},69^{\circ},69^{\circ}\)