Question

The measure of the obtuse angle in the isosceles triangle is two and a half times the measure of one base angle. What are the measures of all the angles?

Answer 1

100, 40, 40

Explanation:

In an isosceles triangle, there are two angles that are the same and one that is different. We know there is one angle that is more than `90^o` because that is the definition of an obtuse angle. We also know that the sum of all the angles of a triangle equal `180^o`. Let's put all this together and find the measures of the angles.

I'm going to call `x` the obtuse angle and `y` the acute angles.

`x+2y=180`

`x=2.5y`

Let's substitute the second equation into the first:

`2.5y+2y=180`

`4.5y=180`

`y=40`

Which means that `x` is:

`x=2.5y`

`x=2.5(40)=100`

Answer 2

`40^circ,40^circand100^circ`

Explanation:

In an Isoceles triangle, the two base angles are equal. Let the base angles be `x`. Then, the obtuse angle would be `2 1/2*x`

We need to find the value of `x`

Since the sum of the angles in a triangle is `180^circ`,

`rarrx+x+2 1/2*x=180^circ`

`rarr2x+2 1/2*x=180^circ`

`rarr2x+5/2*x=180^circ`

`rarr2x+(5x)/2=180^circ`

`rarr(9x)/2=180^circ`

`rarr9x=360^circ`

`color(green)(rArrx=40^circ`

Now we know that the base angles are `color(green)(40^circ`

So, the other angle is `color(orange)(2 1/2*40=100)`