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 answer:

C =  122 °
D =  46 °

Step-by-step explanation:

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

$$\begin{gathered} B+D=180\mathrm{°} \\ D=180-B=180-134=46\text{°} \end{gathered}$$

Try another example

Related math problems and questions:

• 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?
• 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'
• 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?
• 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.
• 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?
• 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 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.
• 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 lay on the circle and divided into arcs in the ratio 7:8:7. 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?
• Circle and hexagon
  Calculate the radius of a circle whose circumference is 8.4 cm longer than the inscribed regular hexagon's circumference.
• 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°?
• Complete construction
  Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.