# Internal and external angles

Calculate the remaining internal and external angles of a triangle, if you know the internal angle γ (gamma) = 34 degrees and one external angle is 78 degrees and 40 '. Determine what kind of triangle it is from the size of its angles.

Correct result:

α =  101.3333 °
β =  44.6667 °
γ =  34 °
α' =  78.6667 °
β' =  135.3333 °
γ' =  146 °

#### Solution:

$\alpha =180-\left(78+40\mathrm{/}60\right)=101.333{3}^{\circ }=10{1}^{\circ }2{0}^{\mathrm{\prime }}$
$\beta =180-\left(180-\left(78+40\mathrm{/}60\right)+34\right)=44.666{7}^{\circ }=4{4}^{\circ }4{0}^{\mathrm{\prime }}$
$\gamma =34=3{4}^{\circ }$
${\alpha }^{\mathrm{\prime }}=78+40\mathrm{/}60=78.666{7}^{\circ }=7{8}^{\circ }4{0}^{\mathrm{\prime }}$
${\beta }^{\mathrm{\prime }}=180-\left(78+40\mathrm{/}60\right)+34=135.333{3}^{\circ }=13{5}^{\circ }2{0}^{\mathrm{\prime }}$
${\gamma }^{\mathrm{\prime }}=180-34=14{6}^{\circ }$

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