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 °.

Explanation:

Step1: Sum of angles in triangle

The sum of angles in a triangle is $180^\circ$. Let base angles be $(2x+3)^\circ$ each. So:
$42 + 2(2x + 3) = 180$

Step2: Simplify the equation

Expand and combine like terms:
$42 + 4x + 6 = 180$
$4x + 48 = 180$

Step3: Solve for x

Subtract 48 from both sides:
$4x = 132$
Divide by 4: $x = 33$

Step4: Calculate base angle

Substitute $x=33$ into $(2x+3)$:
$2(33) + 3 = 69$

Answer:

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