# 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.

Result

C =  122 °
D =  46 °

#### Solution:

$A=58 \ ^\circ \ \\ B=134 \ ^\circ \ \\ \ \\ ∠ 2DCB=DSB_{ 1 } \ \\ ∠ 2DAB=DSB_{ 2 } \ \\ DSB_{ 1 } + DSB_{ 2 }=360 ^\circ \ \\ 2DCB + 2DAB=360 ^\circ \ \\ DCB + DAB=180 ^\circ \ \\ C+A=180 ^\circ \ \\ \ \\ A+C=180 ^\circ \ \\ \ \\ C=180-A=180-58=122=122 ^\circ$
$B+D=180 ^\circ \ \\ \ \\ D=180-B=180-134=46=46 ^\circ$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators

## Next similar math problems:

1. Clock hands
Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours.
2. Clock face
clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
3. Find the 9
Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
4. 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 ".
5. Angles in triangle
The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
6. 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?
7. Pentagon
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
8. Ruler and compass
Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
9. Slope
Find the slope of the line: x=t and y=1+t.
10. Triangle SSA
Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
11. The dormitory
The dormitory accommodates 150 pupils in 42 rooms, some of which are triple and some are quadruple. Determine how many rooms are triple and how many quadruples.
12. Center traverse
It is true that the middle traverse bisects the triangle?
13. Two numbers
We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
14. Reward
Janko and Peter divided the reward from the brigade so that Peter got 5/8 of the reward. What percentage of Janko's reward got?
15. Equations - simple
Solve system of linear equations: x-2y=6 3x+2y=4
16. The ball
The ball was discounted by 10 percent and then again by 30 percent. How many percent of the original price is now?
17. Persons
Persons surveyed:100 with result: Volleyball=15% Baseball=9% Sepak Takraw=8% Pingpong=8% Basketball=60% Find the average how many like Basketball and Volleyball. Please show your solution.