Respuesta :

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Let x = the vertex angle so 30 + x = the base angle. 

The sum of the three angles = 180 degrees. Set up an equation then solve.

x + 30 + x + 30+ x = 180
3x + 60 = 180
Subtract 60 from both sides
3x = 120
Divide both sides by 3
x = 40  =>  =>  Vertex Angle
x + 30 = 70  => => Base Angles

Answer:

The measure of the vertex angle is 24°

Step-by-step explanation:

Suppose, the measure of the vertex angle [tex]=x[/tex]

It is given that each base angle of the isosceles triangle is 30 more than twice the measure of the vertex angle.

So, the measure of each base angle [tex]=2x+30[/tex]

That means, the measures of three angles in the triangle are [tex]x,\ \ 2x+30\ \ and\ \ 2x+30[/tex].

Now we know, the sum of all three angles in any triangle is always 180°. So, the equation will be.....

[tex]x+(2x+30)+(2x+30)=180[/tex]

[tex]5x+60=180\\ \\ 5x=180-60\\ \\ 5x=120\\ \\ x=\frac{120}{5}=24[/tex]

So, the measure of the vertex angle is 24°

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