Question

an exterior angle of an isosceles triangle has measure 130°. find two possible sets of measures for the angles of the triangle.

if the exterior angle of the bases is 130°, then the measure of the angle of each base is \\(\square\\)° and the measure of the vertex is \\(\square\\)°.

Explanation:

Step1: Find the base angle

An exterior angle and its adjacent interior angle are supplementary, so the interior angle (base angle) adjacent to the \(130^\circ\) exterior angle is \(180^\circ - 130^\circ = 50^\circ\).

Step2: Find the vertex angle

In an isosceles triangle, the two base angles are equal. The sum of the interior angles of a triangle is \(180^\circ\). Let the vertex angle be \(x\). Then \(50^\circ + 50^\circ + x = 180^\circ\). Solving for \(x\), we get \(x = 180^\circ - 100^\circ = 80^\circ\).

Answer:

The measure of the angle of each base is \(50^\circ\) and the measure of the vertex is \(80^\circ\).