Question

The vertex angle of an isosceles triangle measures 42°. A base angle in the triangle has a measure given by
(2x + 3)°. What is the value of x? What is the measure of each base angle?

x =

Each base angle measures
°

Answer 1

In an isosceles triangle, the sum of the angles is always 180°. Given that the vertex angle is 42°, the two base angles are equal and can be represented as (2x + 3)°.

Let's denote each base angle as \((2x + 3)^\circ\).

The equation for the sum of the angles in the triangle can be written as:

\[
42 + (2x + 3) + (2x + 3) = 180
\]

Now, simplify the equation:

\[
42 + 2(2x + 3) = 180
\]

\[
42 + 4x + 6 = 180
\]

Combine like terms:

\[
48 + 4x = 180
\]

Next, isolate the \(4x\) term by subtracting 48 from both sides:

\[
4x = 180 - 48
\]

\[
4x = 132
\]

Now, divide by 4 to find \(x\):

\[
x = \frac{132}{4} = 33
\]

Now that we have \(x\), we can find the measure of each base angle:

Substituting \(x = 33\) into the expression for the base angle:

\[
\text{Base Angle} = 2x + 3 = 2(33) + 3 = 66 + 3 = 69°
\]

**Final results:**

\[
x = 33
\]

Each base angle measures \(69^\circ\).