Question

In a right angled triangle on of the acute angles is 20•(degrees) greater than the other. What are the angles of the triangle?

Answer 1

`color(magenta)(90^@, 35^@ and 55^@`

Explanation:

Let the `2` angles be `x and x+20`

`=>x+x+20^@+90^@=180^@` [Angles Sum Property]

`=>2x+110^@=180^@`

`=>2x=70^@`

`color(red)(=>x=35^@`

So, the 2 angles are `x=35^@` & `x+20^@=55^@`

That gives us the 3 angles: `color(magenta)(90^@, 35^@ and 55^@`

`color(blue)("Verification:"`

`90^@+35^@+55^@`

`=180^@` [As per the Angle Sum Property]

~Hope this helps! :)

Answer 2

`color(blue)(55^@ , 35^@ " and " 90^@)`

Explanation:

We know the sum of the angles in a triangle is `180^@`. If we have a right angled triangle, then the sum of the other two angles is `90^@`

Let one of the angles be `theta`

If one angle is `20^@` greater than the other, then:

`theta+(theta+20^@)=90^@`

`2theta=90^@-20^@=70^@`

`theta=(70^@)/2=35^@`

So one angle is `35^@` and the other angle is:

`theta+20^@=>35^@+20^@=55^@`