Each base angle of an isosceles triangle is 30 more than twice the measure of the vertex angle. What is the measure of the vertex angle?

Answer:The measure of the vertex angle is 24°.Step-by-step explanation:Given : Each base angle of an isosceles triangle is 30 more than twice the measure of the vertex angle.To find : What is the measure of the vertex angle?     Solution : Let the measure of the vertex angle be 'x'.According to question,Each base angle of an isosceles triangle is 30 more than twice the measure of the vertex angle.i.e. the measure of each base angle = 2x+30.So, The three angles of an isosceles triangle is [tex]x,2x+30,2x+30[/tex]We know by angle sum property, The sum of all three angles in any triangle is always 180°.[tex]x+(2x+30)+(2x+30)=180[/tex][tex]5x+60=180[/tex][tex]5x=180-60[/tex][tex]5x=120[/tex][tex]x=\frac{120}{5}[/tex][tex]x=24[/tex]Therefore, The measure of the vertex angle is 24°.