Respuesta :
Answer:
The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.
Step-by-step explanation:
Given : The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
To find : The four angles of the quadrilateral are °, °, °, and °, respectively.
Solution : We have given that The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
Let the angle of the quadrilateral is x
Then all the angles are x , 2x , 5x ,4x
Complete angle formed by circle is 360 °
Sum of all the angle are 360
x + 2x + 5x + 4x = 360 .
12 x = 360 .
On dividing both sids by 12.
x = 30 .
Then
2x = 60
5x = 5 * 30 = 150 .
4x = 4 *30 = 120 .
Therefore, The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.
Answer:
for plato users the answers are 45,75,135,105
Step-by-step explanation:
