Question

The diagram below shows an Isosceles triangle. Label the base angles and the vertex

Answer 1

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:

$\mathbf{6a -3 =a + 12}$

Collect like terms

$\mathbf{6a -a =3 + 12}$

$\mathbf{5a = 15}$

Divide both sides by 5

$\mathbf{a = 3}$

Substitute 3 for a in Base = (6a- 3),

$\mathbf{Base = 6 \times 3 - 3}$

$\mathbf{Base = 18 - 3}$

$\mathbf{Base = 15}$

So, the base angle is 15 degrees.

The vertex angle is calculated using:

$\mathbf{Vertex=180 -2 \times Base}$

So, we have:

$\mathbf{Vertex=180 -2 \times 15}$

$\mathbf{Vertex=150 }$

Hence, the vertex angle is 150 degrees

Read more about isosceles triangles at:

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