# One of the measures of the angles of a triangle is 25^circ. If the sum of the measures of the other two angles is 155^circ and the difference between their measures is 5^circ, what are the measures of the unknown angles?

Dec 9, 2016

${80}^{\circ} , {75}^{\circ}$

#### Explanation:

Let the two unknown angles be $a , \mathmr{and} b$, respectively.

$\implies a + b = {155}^{\circ} \ldots \ldots . \left(1\right)$
$\implies a - b = {5}^{\circ} \ldots \ldots \ldots . \left(2\right)$

Adding (1) and (2), we get,
$2 a = {160}^{\circ}$
$\implies a = {80}^{\circ}$

substituting $a = 80$ in (2), we get
$\implies 80 - b = {5}^{\circ}$,
$\implies b = {75}^{\circ}$