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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?

Respuesta :

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
MrRoyal

The base angles of an isosceles triangle are equal.

The value of x is 33, and the measure of each base angle is 69.

The given parameter are:

[tex]\mathbf{Vertex = 42}[/tex]

[tex]\mathbf{Base = 2x + 3}[/tex]

So, we have:

[tex]\mathbf{2x + 3 + 2x +3 + 42 = 180}[/tex]

Collect like terms

[tex]\mathbf{2x + 2x = 180 - 42 - 3 - 3}[/tex]

[tex]\mathbf{4x = 132}[/tex]

Divide both sides by 4

[tex]\mathbf{x = 33}[/tex]

Recall that:

[tex]\mathbf{Base = 2x + 3}[/tex]

So, we have:

[tex]\mathbf{Base = 2(33) + 3}[/tex]

[tex]\mathbf{Base = 69}[/tex]

Hence, the value of x is 33, and the measure of each base angle is 69.

Read more about isosceles triangle at:

https://brainly.com/question/21495359

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