Triangle angles

In a triangle, ABC, the interior angle at vertex C is twice the internal angle at point A. The outer angle at point B measured 117 degrees. How big is the external angle at vertex A?

Correct answer:

a =  39 °

Step-by-step explanation:


a+b+c=180
c = 2a
180-b = 117

a+b+c=180
c = 2•a
180-b = 117

a+b+c = 180
2a-c = 0
b = 63

a = 39
c = 78

Our linear equations calculator calculates it.



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar







Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our trigonometric triangle calculator.

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: video1

Related math problems and questions:

  • Internal angles
    triangle Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at vertex A.
  • Angles
    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?
  • Interior angles
    circle_inscribed_polygon In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles.
  • Outer angles
    triangle_1111 The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertex B is 136°50'. What size has the inner triangle angle at the vertex C?
  • Internal and external angles
    inner_outer_angles_triangle 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.
  • Alfa, beta, gama
    angles_in_triangle In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
  • Angle at the apex
    iso In an isosceles triangle, the angle at the apex is 30° greater than the angle at the base. How big are the internal angles?
  • Angles of the triangle
    angles ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
  • In triangle
    triangle In triangle ABC, the magnitude of the internal angle gamma is equal to one-third of the angle alpha. The size of the angle beta is 80 degrees larger than the size of the gamma angle. Calculate the magnitudes of the interior angles of the triangle ABC.
  • Internal angles
    angle One internal angle of the triangle JAR is 25 degrees. The difference is the size of the two others is 15°. Identify the size of these angles.
  • Angles
    triangle The triangle is one outer angle 158°54' and one internal angle 148°. Calculate the other internal angles of a triangle.
  • Inner angles
    rr_triangle3 The magnitude of the internal angle at the main vertex C of the isosceles triangle ABC is 72°. The line p, parallel to the base of this triangle, divides the triangle into a trapezoid and a smaller triangle. How big are the inner angles of the trapezoid?
  • Angles ratio
    3angle In a triangle ABC, is true relationship c is less than b, and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is:
  • Angles in ratio
    angles The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.
  • The second
    triangle The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
  • Angles in a triangle
    fun The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
  • Angles of a triangle
    triangles In 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.