Question

solving for angle measures of isosceles triangles
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 °.

Explanation:

Step1: Sum of triangle angles is 180°

Let each base angle be $\theta = (2x+3)^\circ$. The vertex angle is $42^\circ$, so:
$$42 + 2\theta = 180$$

Step2: Solve for base angle $\theta$

$$2\theta = 180 - 42$$
$$2\theta = 138$$
$$\theta = \frac{138}{2} = 69$$

Step3: Set equal to $(2x+3)$ and solve for $x$

$$2x + 3 = 69$$
$$2x = 69 - 3$$
$$2x = 66$$
$$x = \frac{66}{2} = 33$$

Answer:

$x = 33$
Each base angle measures $69^\circ$.