IDNLearn.com is the place where your questions are met with thoughtful and precise answers. Discover reliable and timely information on any topic from our network of experienced professionals.
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