Question

The ratio of the measure of the vertex angle is to the base angle of an isosceles triangle is 8:5. Find the measure do the vertex angle ?

Answer 1

8x + 5x + 5x = 180
18x = 180
x = 10

the measure of the vertex angle = 8x = 8*10 = 80°

Answer 2

Answer:

We now that all three intern angles must sum 180°, by definition.

Also, we know that the pair of angles at the base of the triangle must be equal.

So, if the ratio is 8:5, we could say that the base angles are expressed as $5x$, and the third angle would be $8x$, because they are in the ratio 8:5.

Therefore, the expression to find the answer would be:

$8x+5x+5x=180\°$

Solving for $x$, we have:

$18x=180\°\\x=\frac{180}{18}\\x=10\°$

To prove that this is the right answer, we replace this value in each angle expression:

$5x=5(10)=50\\8x=8(10)=80$

So, the sum of angles would be:

$50+50+80=180$

As you can see, the answer is correct, because their sum results in 180.

Therefore, the vertex angle is 80° and each base angle is 50°.