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?

Answer 1

The 2  base angles are equal so  the measure of 1 base angle = (180 - 42) / 2
=  69 degrees

2x + 3 = 69
2x = 66
x = 33

each base angle measures 69 degrees

Answer 2

Part a)

we know that

An isosceles triangle has two base angles that are congruent

The sum of two base angles plus the vertex angle is equal to $180$ degrees

so

In this problem

$vertex\ angle=42\°$

$base\ angle=(2x+3)\°$

$42\°+2*(2x+3)\°=180\°$

Solve for x

$42+4x+6=180$

$4x=180-48$

$x=132/4$

$x=33\°$

therefore

the answer part a) is

the value of x is $33\°$

Part b) What is the measure of each base angle?

we know that

$base\ angle=(2x+3)\°$

we have that

$x=33\°$

substitute the value of x in the equation

$base\ angle=(2*33+3)\°$

$base\ angle=69\°$

therefore

the answer part b) is

the measure of each base angle is $69\°$