Question

If the two acute angles of a right triangle have measures (2x-11) and (x+26) , then what is the value of X

Answer 1

ANSWER


`x = 25 \degree`

EXPLANATION


The sum of the interior angles of a triangle is

`180 \degree.`





In a right angle triangle, one of the angles is already

`90 \degree.`



Therefore the remaining two acute angle will add up to

`90 \degree.`


This implies that,


`(2x - 11) + (x + 26) = 90 \degree`



We group like terms to get,


`2x + x + 26 - 11 = 90`


This gives us,


`3x + 15 = 90`


This gives,



`3x = 90 - 15`



`3x = 75`

We divide both sides of the equation by 3 to obtain,


`x = 25 \degree`