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,

$x = 25 \degree$