Question

1. the measure of the vertex angle of an isosceles triangle is 70. find the measure of a base angle of the triangle.

Explanation:

Step1: Recall the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the measure of each base angle be \(x\). In an isosceles triangle, the two base angles are equal. The vertex angle is given as \(70^{\circ}\). So, we can write the equation \(x + x+70 = 180\).

Step2: Simplify the equation

Combine like terms: \(2x+70 = 180\).
Subtract \(70\) from both sides of the equation: \(2x=180 - 70\).
So, \(2x = 110\).

Step3: Solve for \(x\)

Divide both sides of the equation \(2x = 110\) by \(2\). We get \(x=\frac{110}{2}\).

Answer:

\(55^{\circ}\)