The base angles of an isosceles triangle are equal
The base angles are 15 degrees, while the vertex angle is 150 degrees
The base angles are given as:
Base = (6a- 3) and (a + 12)
So, we have:
[tex]\mathbf{6a -3 =a + 12}[/tex]
Collect like terms
[tex]\mathbf{6a -a =3 + 12}[/tex]
[tex]\mathbf{5a = 15}[/tex]
Divide both sides by 5
[tex]\mathbf{a = 3}[/tex]
Substitute 3 for a in Base = (6a- 3),
[tex]\mathbf{Base = 6 \times 3 - 3}[/tex]
[tex]\mathbf{Base = 18 - 3}\\[/tex]
[tex]\mathbf{Base = 15}[/tex]
So, the base angle is 15 degrees.
The vertex angle is calculated using:
[tex]\mathbf{Vertex=180 -2 \times Base}[/tex]
So, we have:
[tex]\mathbf{Vertex=180 -2 \times 15}[/tex]
[tex]\mathbf{Vertex=150 }[/tex]
Hence, the vertex angle is 150 degrees
Read more about isosceles triangles at:
https://brainly.com/question/25739654
