Outer angles

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?

Correct answer:

C =  28.5 °

Step-by-step explanation:

$$\begin{gathered} A=180-(71+40\mathrm{/}60)={\displaystyle \frac{325}{3}}\doteq 108.3333\text{ ° } \\ B=180-(136+50\mathrm{/}60)={\displaystyle \frac{259}{6}}\doteq 43.1667\text{ ° } \\ C=180-(A+B)=180-(108.3333+43.1667)=28.5\text{°}=28\mathrm{°}30^{\mathrm{\prime }} \end{gathered}$$

Try another example

Related math problems and questions:

• Triangles
  Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
• 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?
• Angles
  The triangle is one outer angle 158°54' and one internal angle 148°. Calculate the other internal angles of a triangle.
• Gamma angle
  Find the magnitude of the gamma angle in triangle ABC if: α = 38° 56 ’and β = 47° 54’.
• MO Z7–I–6 2021
  In the triangle ABC, point D lies on the AC side and point E on the BC side. The sizes of the angles ABD, BAE, CAE and CBD are 30°, 60°, 20° and 30°, respectively. Find the size of the AED angle.
• Inner angles
  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?
• Main/central vertex
  ABC is an isosceles triangle with base BC and main vertex A. The angle at vertex A is 18°. What will be the size of the angle at vertex B?
• Internal angles
  The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete
• Elevation angles
  From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain?
• Angles of a triangle
  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.
• Right angle
  In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
• 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 ".
• 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.
• The two
  The two angles of a triangle are 78° and 82°. So what is the measure of the remaining third angle?
• The triangles
  The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '.
• Angles in ratio
  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.
• Powerplant chimney
  From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney?