# 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:

$\alpha =180-\left(78+40\mathrm{/}60\right)=101.333{3}^{\circ }=10{1}^{\circ }2{0}^{\mathrm{\prime }}$
$\beta =180-\left(180-\left(78+40\mathrm{/}60\right)+34\right)=44.666{7}^{\circ }=4{4}^{\circ }4{0}^{\mathrm{\prime }}$
$\gamma =34=3{4}^{\circ }$
${\alpha }^{\mathrm{\prime }}=78+40\mathrm{/}60=78.666{7}^{\circ }=7{8}^{\circ }4{0}^{\mathrm{\prime }}$
${\beta }^{\mathrm{\prime }}=180-\left(78+40\mathrm{/}60\right)+34=135.333{3}^{\circ }=13{5}^{\circ }2{0}^{\mathrm{\prime }}$
${\gamma }^{\mathrm{\prime }}=180-34=14{6}^{\circ }$ We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you! Tips to related online calculators

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Angles in triangle Calculate the alpha angle in the triangle if beta is 61 degrees and 98 gamma degrees. The size of two internal angles of a triangle ABC are α=6/18π and β=7/18π. Calculate the size of the third angle.
• Angles of a triangle In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
• Construction Construction the triangle ABC, if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60° and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction)
• Angles The outer angle of the triangle ABC at the vertex A is 114°12'. The outer angle at the vertex B is 139°18'. What size is the internal angle at the vertex C?
• Outer angles The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertx B is 136°50'. What size has the inner triangle angle at the vertex C?
• Complementary angles Two angles are complementary. If one angle measures 10°, what is the measure of the second angle?
• The sides 3 The sides of an equilateral triangle are 9.4 cm, correct to the nearest one decimal place. Work out the upper bound of the side of this triangle
• Find the 9 Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
• Similarity coefficient The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ".
• Type of triangle How do I find the triangle type if the angle ratio is 2:3:7 ?
• Triangle ABC Construct a triangle ABC is is given c = 60mm hc = 40 mm and b = 48 mm analysis procedure steps construction
• Diagonal Can a rhombus have the same length diagonal and side? Convert magnitude of the angle α = 136°18'10" to radians: Determine the percentage rate of keeper interventions if from 32 shots doesn't caught four shots. It is true that the middle traverse bisects the triangle? How many three-digit odd numbers divisible by 5, which are in place ten's number 3?