# A triangle has angles of 78°, 47°, and x+65°. What is the value of x?

Oct 8, 2016

$x = - 10$

#### Explanation:

Since the interior angles of all triangles add up to ${180}^{o}$, you have to set up an equation that is equal to ${180}^{o}$

${78}^{o} + {47}^{o} + \left(x + {65}^{o}\right) = {180}^{o}$

Combine like terms

${78}^{o} + {47}^{o} + {65}^{o} = {190}^{o}$

$x + {190}^{o} = {180}^{o}$

Isolate x by subtracting ${190}^{o}$ on both sides of the equation

$x = - 10$

To check the answer, plug -10 back in for x

${78}^{o} + {47}^{o} + \left(- 10 + {65}^{o}\right) = {180}^{o}$

${125}^{o} + {55}^{o} = {180}^{o}$