Interior angles

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.

Correct result:

C =  122 °
D =  46 °

Solution:

$$\begin{gathered} A=58^{\circ } \\ B=134^{\circ } \\ \mathrm{\angle }2DCB=DS{B}_1 \\ \mathrm{\angle }2DAB=DS{B}_2 \\ DS{B}_1+DS{B}_2=360^{\circ } \\ 2DCB+2DAB=360^{\circ } \\ DCB+DAB=180^{\circ } \\ C+A=180^{\circ } \\ A+C=180^{\circ } \\ C=180-A=180-58=122^{\circ } \end{gathered}$$

$$\begin{gathered} B+D=180^{\circ } \\ D=180-B=180-134=46^{\circ } \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Triangle angles
  In a triangle ABC the interior angle at the vertex C is twice as the internal angle at the point A. Outer angle at the point B measured 117 degrees. How big is the outer angle at the vertex A?
• Clock hands
  Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours.
• 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?
• 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?
• Internal angles
  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 the vertex A.
• 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.
• RT - inscribed circle
  In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
• Circle section
  Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and
• Inscribed triangle
  To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
• Circumferential angle
  Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC.
• Hexagon in circle
  Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle.
• Angles
  The triangle is one outer angle 158°54' and one internal angle 148°. Calculate the other internal angles of a triangle.
• angles in quadrilateral
  What size have angles in quadrilateral (4-gon) if they are in a ratio of 8: 9: 10: 13?
• Regular n-gon
  In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
• The chord
  The side of the triangle inscribed in a circle is a chord passing through the circle center. What size are the internal angles of a triangle if one of them is 40°?
• Circle and hexagon
  Calculate the radius of a circle whose circumference is 8.4 cm longer than the circumference of the inscribed regular hexagon.